The diagonal of a rectangle is thrice its smaller side. The ratio of its sides is

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08 Mar 2013 rectangle

The diagonal of a rectangle is thrice its smaller side. The ratio of its sides is

OPtion

1) sqrt2 : 1
2) 2 sqrt2 : 1
3) 1 : 2
4) 3 : 2
5) sqrt3 : 1
6) 3 : 2
7) 2 : 3
8) sqrt3 : 2
9) 1 : 3 sqrt2
10) None of these

Solution

let the smaller side be x
then diagonal is 3x
by using pythagoras theorem
largest side is 2(sqrt2)x
then the ratio of side
2(sqrt2)x : x
therefore 2 sqrt2 : 1
option no 2

Correct Option: 2 Best Solution (17)

sumit jindal   11 years AGO

a^2+b^2=(3*b)^2
a^2=8*b^2
a=2sqrt2*b
a:b=2sqrt2:1

Like? Yes (24) | No (8)  

sandhya suman   11 years AGO

let smaller side=a bigger side=b so diagonal=3a
so b=a sqrt(9-1)=2a sqrt2
so ratio =2 sqrt2:1

Like? Yes (6) | No (2)  

Sanjeewani Indurkar   11 years AGO

let smaller side be x and greater side be y. Then as per given condition diagonal=3x.
Then according to pythagoras theorem,
x^2+y^2=9(x^2)
8(x^2)=y^2
taking square root
y:x =2 sqrt2:1

Like? Yes (6) | No (3)  

krishnapriya   11 years AGO

let x be smaller side
then diagonal=3x
Using Pythagorus Theorem,
other side of the rectangle=sqrt((3x)^2-x^2)
=sqrt(8x^2)=xsqrt(8)
Then the ratio is
xsqrt(8):x
sqrt(8):1
2sqrt(2):1

Like? Yes (3) | No (4)  

ABHIRUCHI SHARMA   11 years AGO

Let the width be x and diagonal is 3x then length
will be 2xsqrt2.the ratio will be 2sqrt2:1

Like? Yes (3) | No (5)  

deepika   11 years AGO

let a be the smallest side and b is the other.
diagonal=sqrt(a*a+b*b)=3a
a*a+b*b=9 a*a
b*b=8a*a
b=2sqrt2 a
then ratio will be2sqrt2 a:a
2sqrt2:1

Like? Yes (3) | No (5)  

Vinay Sipani    11 years AGO

a^2 + b^2 = d^2

d = 3a => a^2 + b^2 = 9a^2
=> 8a^2 = b^2
=> b : a = 2sqrt2 : 1

Like? Yes (4) | No (7)  

MONIKA JAIN   11 years AGO

given that:d=3b
d=sqrt(sql+sqb)=3b
sql+sqb=9*sqb
sql=8*sqb
sql/sqb=8/1
l/b=sqrt(8/1)
l/b=2*sqrt2/1
so,ratio of sides of rectangleis:l/b=2*sqrt2:1
so,answer option is 2.

Like? Yes (2) | No (6)  

Balakumaran N.A   11 years AGO

et x be smaller side of rectangle, Then diagonal = 3x
Using Pythagorean theorem, other side of rectangle = √(9x² - x²) = √(8x²) = √(8)x

Ratio:
x : √8 x
1 : √8
1 : 2√2

Like? Yes (1) | No (5)  

Devendra Marghade   11 years AGO

If shortest side=x, longest side=y
Given diagonal=3x
(3x)^2=y^2+x^2
y^2=8x^2
y/x : (2 sqrt2)/1

Like? Yes (2) | No (6)  

jai prakaash   11 years AGO

let smaller side be x so the diagonal is 3x
then the other side will be sqrt(9x^2-x^2)
i.e 2sqrt2x
so the ratio is 2sqrt2:1

Like? Yes (4) | No (8)  

AVINASH KUMAR   11 years AGO

let l and b be the sides of rectangle in which b is smaller side.
now according to question
l^2+b^2=(3b)^2
l^2=8b^2
l= 2*sqrt2*b
now ratio of sides is
l/b=2*sqrt2*b/b=2*sqrt2

Like? Yes (1) | No (5)  

amit   11 years AGO

diagonal of rectangle is=sqrt(a^2+b^2)
if smaller side b then sqrt(a^2+b^2)=3*b
so a/b=2sqrt2
so 2nd option

Like? Yes (1) | No (5)  

srinivasulareddy   11 years AGO

suppose smaller side say b and larger is a then
3b=sqrt(a^2+b^2)
9b^2=a^2+b^2
8b^2=a^2
b^2/a^2=1/8
a^2/b^2=8/1
a/b=2sqrt2/1

Like? Yes (3) | No (7)  

Rupendra Sahu   11 years AGO

let length is a and width is b,
then diagonal=(a^2+b^2)^1/2=3a
so b=(2*2^1/2)a,
so ratio will b 2*2^1/2 : 1

Like? Yes (1) | No (5)  

Nakul Devadas   11 years AGO

Pytha goras thearom.
length = sqrt(9x^2-x^2) = 2*sqrt2
So the ratio is 2*sqrt2:1.

Like? Yes (1) | No (5)  

jitendra singh   11 years AGO

smaller=a
digonal=3a

Like? Yes (1) | No (6)