Akanksha Mishra   11 years AGO

the diameter of the circle is also the diagonal of the rectangle, which means it's the hypotenuse of two congruent right triangles.

the two sides of the triangle (or rectangle) sum to 17 since they are half of the perimeter.

let x = one side
17 - x = the other side

use the Pythagorean theorem:

x^2 + (17 - x)^2 = 13^2

x^2 + 289 - 34x + x^2 = 169

2x^2 - 34x + 120 = 0

x^2 - 17x + 60 = 0

(x - 5)(x - 12) = 0

x = 5 or x = 12

the sides of the rectangle are 5 and 12 units.

that's it! ;)

Like? Yes (15) | No (6)  

ROHIT UPADHYAY   11 years AGO

the diameter of the circle is also the diagonal of the rectangle
the two sides of the rectangle sum to 17 since they are half of the perimeter.

let x = one side
17 - x = the other side

use the Pythagorean theorem:

base^2+height^2=hypotenuse^2

x^2 + (17 - x)^2 = 13^2

x^2 + 289 - 34x + x^2 = 169

2x^2 - 34x + 120 = 0

x^2 - 17x + 60 = 0

(x - 5)(x - 12) = 0

x = 5 or x = 12

Like? Yes (9) | No (6)  

pratibha Tiwari    11 years AGO

The diameter of the circle is the
diagonal of the rectangle.
The width and length of the
rectangle and the diagonal form a
right triangle.
From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169
The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w
Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0
Factor
(w - 5)(w - 12) = 0
w = {5, 12}
Plugging into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12
The rectangle is 5 units by 12
units

Like? Yes (3) | No (1)  

Jigyasa Kumar   11 years AGO

Answer : 5 by 12 units
The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorus theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12
keeping into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (4) | No (3)  

Aditya Verma   11 years AGO

simple perimeter of a rectangle is = 2*(l+h)
now cross check then we get the single answer to satisfy above equation that is 5 and 12
2*(5+12)=34
answer is option 5

Like? Yes (5) | No (4)  

Leelanand Kumar Yalla   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
So, according to Hypotenus Theorem;
Hyp^2 = (Length)^2+(Breadth)^2;
169= (Length)^2+(Breadth)^2;------->(1)
Perimeter of a Rectangle is 2(L+B)= 34;------->(2)
L+B= 17;
17-L= B;
Substitute in Above Equation (1)
169= (L)^2+(17-L)^2;
L^2+289+L^2-34L = 169;
2L^2-34L+120=0;
L=5,12;
SUBSTITUTE IN (2);
2(5+B)= 34;
Therefore B=12;
Therefore The sides of a rectangle are 5,12......

Like? Yes (1) | No   

KRISHNAN   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12}

Plugging into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (2) | No (1)  

Rahul gulati   11 years AGO

Firstly, Only 5,12 is the combination of sides which gives perimeter as 34.

On further checking, if its in a circle then:
(5/2)^2 + (12/2)^2 = (13/2)^2

This is satisfied, hence it is a correct answer.

Like? Yes (1) | No   

NILOTPAL MRINAL   11 years AGO

the two sides of the triangle (or rectangle) sum to 17 since they are half of the perimeter.

let x = one side
17 - x = the other side

use the Pythagorean theorem:

x^2 + (17 - x)^2 = 13^2

x^2 + 289 - 34x + x^2 = 169

2x^2 - 34x + 120 = 0

x^2 - 17x + 60 = 0

(x - 5)(x - 12) = 0

x = 5 or x = 12

the sides of the rectangle are 5 and 12 units.

Like? Yes (2) | No (1)  

vigneshwari   11 years AGO

given that, diameter of the circle = 13
and, rectangle is inscribed in the circle;
so that, diagonal of the rectangle = 13
that is, sqrt(l^2 + b^2) = 13
(l^2 + b^2) = 169....(1)
Given that, perimeter = 2(l+b) = 34
(l+b) = 17
(l+b)^2 = 289
l^2 + b^2 + 2lb = 289
from (1), we have,
169 + 2lb = 289
2lb = 120 => lb = 60 ...(2)
Solving (1) and (2), we get,
(l,b) = (12,5).

Like? Yes (1) | No   

NEERAV KHANDELWAL   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12}

Plugging into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (2) | No (1)  

ANU   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12}

Plugging into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (3) | No (2)  

navneet shankhwar   11 years AGO

perimeter of rectangle is 34 then side will be 12 and 5
therfore, 12+5+12+5=34

Like? Yes (2) | No (1)  

Praveen kumar   11 years AGO

draw the diagram!

the diameter of the circle is also the diagonal of the rectangle, which means it's the hypotenuse of two congruent right triangles.

the two sides of the triangle (or rectangle) sum to 17 since they are half of the perimeter.

let x = one side
17 - x = the other side

use the Pythagorean theorem:

x^2 + (17 - x)^2 = 13^2

x^2 + 289 - 34x + x^2 = 169

2x^2 - 34x + 120 = 0

x^2 - 17x + 60 = 0

(x - 5)(x - 12) = 0

x = 5 or x = 12

the sides of the rectangle are 5 and 12 units.

that's it! ;)

Like? Yes (2) | No (1)  

sravani   11 years AGO

12+5=17
2*17=34.
more over sides must be < 13.

Like? Yes (1) | No   

VISHNUVARDHANA   11 years AGO

If rectangle inscribed in a circle if and only if both the sides of rectangle will less than the diameter of circle
here 12,5 satisfy the perimeter 2*(5+12) = 34

so correct option is 5

Like? Yes (1) | No   

pankaj chandra joshi   11 years AGO

diaa= 13=diagonal of rectngl
pythagoras thorm
13^2=a^2+b^2
also (a+b)^2=a^2+b^2+2*ab
givn 2*(a+b)=34
a+b=17
PUT VALUE ABOVE
AB=60
A+B=17
a=12 b=5

Like? Yes (1) | No   

Chandni Maurya   11 years AGO

ans=>w=5,L=12
let w,L are width and length resp.
since it lies inside the circle of 13 unit dia.
=> the diagonalof rectangle will be 13 unit
=>as given 2(W+L)=34
=> W+L= 17---(1)
also, W^2 + L^2= 13^2---(2) (for the triangle made by diagonal)
by trial and error method we can get easily
5+12=17 will satisfy the condition
ans=>w=5,L=12

Like? Yes (1) | No   

palak diwan   11 years AGO

diameter= x*x+y*y = 13*13
2(x+y)= 34
y=12 or 5
x=5 or 12

Like? Yes (1) | No   

RAKESH   11 years AGO

as 5^2+12^2=13^2

Like? Yes (1) | No   

kishore   11 years AGO

2(12+5)=34

Like? Yes (1) | No   

IFFAT IRAM   11 years AGO

a+b=17
b=17-a
d^2=a^2+(17-a)^2
169=a^2+289+a^2-34a
2a^2-34a+120=0
a^2-17a+60=0
(a-5)(a-12)=0
5,12

Like? Yes (1) | No   

P.SWETHA   11 years AGO

sum of l+b=17 we can check from options,also diameter =13 ==> diagonal of a rectangle = 13
so by using Pythagoras theorem l^2+b^2=(13)^2
==>5^2+12^2=25+144=169.

Like? Yes (1) | No   

sai pavan   11 years AGO

ans is 5
Given that
Perimeter of rectangle = 34 =2(Length+Width)
Diameter of circle=13

so Length+width=34/2=17
from the option 5 5+12=17

Checking with diameter of circle
sqrt(5^2+12^2)=>sqrt(169)=13
So No doubt ans is option 5

Like? Yes (1) | No   

vishal singh thapa   11 years AGO

perimeter=2*(l+b)=34
l+b=17 ......eq(1)
and taking diameter of the circle eill be the diagonal of rectangle.
hence in right angle triangle thus formed;we get by pithagorian theorem
l^2+b^2=diagonal^2
l^2+(17-l)^2=13^2 [from eq(1)]
l^2+289+l^2-34l=169
2l^2-34l+120=0
l^2-17l+60=0
l^2-12l-5l+60=0
(l-5)*(l-12)=0
l=5,12
hence
b=12,5. [from eq(1)]
hence option 5 is correct.

Like? Yes (1) | No   

Siba Kumar Sahu   11 years AGO

perimeter of rectangle= 2(a+b) where a & b are sides of rectangle
so p=2(a+b)=34
(a+b)=17
since rectangle is inscribed in a circle of dia 13 unit so by pythagoras theorem, a^2+b^=13^2 only 12 & 5 of sides
of rectangle possible.
so option 5 is correct.

Like? Yes (1) | No   

G.veeranjaneya vara prasad   11 years AGO

12+5=17 by substitute this in 2(a+b) we will get 34.it is also satisfy circle equation also

Like? Yes (2) | No (1)  

saranya sankar   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12}

Plugging into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (1) | No   

saluwaji shushma   11 years AGO

given rectangle perimeter is 34.
we know dat rectangle perimeter =2(l+b)
so 2(l+b)=34
now we substitute the options in the above formula to satisfy the above condition. here 5th option is enough.

Like? Yes (1) | No   

saurabh anand   11 years AGO

here rectangle is inscribed in circle.
Let length be a and breadth be b.
as, perimeter of rectangle = 34 units
so, a + b = 17 units....... equ(1)

as, length of diameter = 13 units
so, by following pythagoras theoram; where diameter as hypotenus of the right triangle and length and breadth be right angling sides.
a^2 + b^2 = 13^2.......... equ(2)

so, only possible combination for equ (1) & equ (2) is 5 and 12 units.
so, option 5 is correct.

Like? Yes (2) | No (2)  

abhilasha   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorus theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12
keeping into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (1) | No (1)  

Aarush Singh   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.

From the pythagorus theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169

The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w

Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0

Factor
(w - 5)(w - 12) = 0

w = {5, 12
keeping into
2w + 2l = 34
2(5) + 2l = 34
10 + 2l = 34
2l = 12
l =12

The rectangle is 5 units by 12 units

Like? Yes (3) | No (3)  

Gurmeet Singh   11 years AGO

Options are silly just by looking at the options you have 2(l+b)=34 for 12 and 5 :D
Moreover l should be less than 13.

Like? Yes (1) | No (1)  

sudipta sadhukhan   11 years AGO

as diametre 13 unts

so 13^2=5^2+12^2

Like? Yes (1) | No (1)  

Ashutosh Nilesh Ujwala Patkar   11 years AGO

perimeter of a rectangle is 2[length + breath]
therefore here length +breadth = 17 units
as 12+5 =17 therefore sides are 12 and 5
as to verify it
6^2+ 2.5^2= radius^2[by pythagoras theorem]
36+6.25=6.5^2
42.25=42.25
ans = 12,5

Like? Yes (1) | No (1)  

Gopal   11 years AGO

perimeter = 34
so add of sides = 17
here (5)^2+(12)^2=(13)^2

Like? Yes (3) | No (3)  

Surya Narayana K   11 years AGO

Diameter of circle = Diagonal of Rectangle
Let L be the length and B be the Breadth of rectangle then
L^2 + B^2 =169 and 2(L+B)=34

The possible solution above two equations is L=12 and B=5.
so it sides are 5,12 units (Option 5)

Like? Yes (1) | No (1)  

Naveen Pandey   11 years AGO

a^2+b^2=169
a+b=17..
solving we get a,b=12,5

Like? Yes (3) | No (3)  

mahima srivastava   11 years AGO

diameter is 13 so none of the side can be more than 13 units
all the other options have value more than except option 5 ie. 5,12 units
moreover 2(5+17)=34
and 34 is the perimeter of rectangle
so option 5

Like? Yes (1) | No (1)  

stutisahoo   11 years AGO

sum of sides is half of perimrter

Like? Yes (2) | No (2)  

TAREK HAYDER SK   11 years AGO

perimeter=34; so x+y=17;x^2+y^2=13^2
so, x=12,y=5(as 169=144+25)

Like? Yes (1) | No (1)  

Doddi Venkata Rao   11 years AGO

2(l+b)=34


so,l+b=17

Like? Yes (1) | No (1)  

Sukanya   11 years AGO

The sides will be less than the diameter as it is inscribed inside the circle.
So from the options 5,12
The perimeter =2(l+b)=2(12+5)=34 is the correct option.

Like? Yes (1) | No (1)  

Parveen Soni   11 years AGO

a+b=34/2=17......... (1)
a^2+b^2=13^2..........(2)
solving 1 & 2 we have
a-b= -7 or +7 and ab=60
hence option 5

Like? Yes (2) | No (2)  

ashu baweja   11 years AGO

as perimeter =34
2(l+b)=34
l+b= 17
apply pythagoras theorem in rectangle where hypatoneus is the diagonal
diadonal^2 = l^2 + b^2
13^ = l^2 + b^2

as l+b =17
therefore on solving equation l=12 ,b=5

Like? Yes (3) | No (3)  

Sourish Barman   11 years AGO

the diagonal of rectangle is = the diameter of circle is 13 units so applying pythagoras theorem
the two sides of rectangle are 5 and 12 as 5^2+12^2=13^2=13 so 5 length=12 breadth =5.

Like? Yes (1) | No (1)  

MD JARJIS HOSSAIN   11 years AGO

2(a+b)=34
=>a+b=17
now trial and error method a=5 & b=12

Like? Yes (1) | No (1)  

kumari julie   11 years AGO

as we know diagonal of rectangle is the diameter of the circle so from pythagores theorem,a^2+b^2=169....(1)
and 2(a+b)=34.....(2)
after solving these equ we get the ans a=12 and b=5
where a nd b are the sides of the rectangle.

Like? Yes (1) | No (1)  

sonali jha   11 years AGO

perimeter=34 that means 2(l+b)=34 => l+b=17
so 5+12=17

Like? Yes (1) | No (1)  

Sudipta Mukherjee   11 years AGO

5^2+12^2=169 ,

Like? Yes (1) | No (1)  

samrat nayak   11 years AGO

perimeter 34 meter
so length+width of rectangular= 17 meter
as diameter of circle is 13 meter = diagonal of rectangle
so 12 and 5 is the correct
12^2 +5^2 = 13^2

Like? Yes (1) | No (1)  

Sneha   11 years AGO

The diameter of the circle is the diagonal of the rectangle.
The width and length of the rectangle and the diagonal form a right triangle.
From the pythagorean theorem
w^2 + l^2 = 13^2
w^2 + l^2 = 169
The perimeter of the rectangle
2w + 2l = 34
w + l = 17
l = 17 - w
Substituting
w^2 + (17 - w)^2 = 169
w^2 + 289 - 34w + w^2 = 169
2w^2 - 34w + 289 = 169
2w^2 - 34w + 120 = 0
w^2 - 17 + 60 = 0
Factor
(w - 5)(w - 12) = 0
w = {5, 12}
The rectangle is 5 units by 12 units

Like? Yes (1) | No (1)