If the area of the larger square is subtracted from twice the area of the smaller square, then the r

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30 Mar 2016 Sides of the two squares

If the area of the larger square is subtracted from twice the area of the smaller square, then the result is 8 cm^2. However, if 3 times the area of the smaller square is added to 2 times the area of the larger square, then the result is 236 cm^2. Determine the side of the two squares.

OPtion

1) 8cm, 14cm
2) 2cm, 6cm
3) 4cm, 10cm
4) 2cm, 4cm
5) 4cm, 8cm
6) 6cm, 8cm
7) 8cm, 10cm
8) 6cm, 10cm
9) 8cm, 12cm
10)4cm, 6cm

Solution

Let the side of the smaller be x cm and side of the larger square be y cm. Then
According to the question, we get
2x^2 - y^2 = 8
=> y^2 = 2x^2 - 8 (i)
Also
3x^2 + 2y^2 = 236
By using (i)
x^2 = 36
x = + - 6 (Rejecting -6)
x = 6
Therefore x = 6
y^ = 64
y = 8
x(smaller) = 6, y(larger) = 8
Option 6)

Correct Option: 6 Best Solution (19)

dev   8 years AGO

let area of small square = s
and area of large square = b

according to question,'
2*s - b = 8 ------(I)
3*s + 2*b = 236 -------(II)

solving this two equation we will get
s= 36
b= 64

since Area = side* side
so side of small square = 6 cm
& side of bigger square = 8 cm

so option (6)

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stuti patel   8 years AGO

let d ar (smaller sq)=x2
and let ar (larger sq) = y2
2x2 - y2 = 8 (1)
3x2+2y2=236 (2)
from 1
-y2 = 8 - 2x2
y2 = 2x2 - 8 (3)

putting 3 in 2
we get
3x2 +2x2-8=236
5x2 = 244
x2 = 48.5
x= 6.9 (4)
now subs val of x
72 - y2 = 8
y2 = 80
y = 8.9

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Nandkishor jaiswal   8 years AGO

let large square side is ---- a
and small square side is --- b
from the equation :--
2*b^2 - a^2 = 8 cm^2 ---------------------1)
b*b^2 + 2*a^2 = 236 cm^2---------------2)
so from the equation (1) and (2)
we get a = 8 cm and b = 6 cm
so the sides will be 6 cm and 8 cm

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Mukund Manohar   8 years AGO

Let a & A be the sides of smaller square and larger square respectively.
Now,2(a^2)-A^2=8……(i)
And 3(a^2)+2(A^2)=236……(ii)
Multiplying (i) by 2 and adding it to (ii),we get
7(a^2)=252
a^2=36
a=6 cm
Substituting the value of a in (i),we get
A^2=64
A=8 cm
Side of smaller square is 6 cm and that of larger square is 8 cm

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Dileep Kumar Gupta   8 years AGO

let side of smaller square =a
and side of larger square =b
according to question

2a^2-b^2=8 .... (1)

3a^2+2b^2=236 .... (2)

solving (1) and (2)

a=6
b=8.

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MRITUNJAY   8 years AGO

2b^2-a^2=8
3b^2+2a^2=236
solve the equation we get a=8
b=6
option 6

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Akshat Sood   8 years AGO

Let the areas be x^2(large square) and y^2(small square)
Then
2y^2-x^2=8
3y^2+4x^2=236
Solve
x=8cm and y=6cm

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Mridula Shaw   8 years AGO

Let,
Area of small square=a^2
Area of large square=A^2
So,
3a^2 + 2A^2 =236-----------Eq I
2a^2 - A^2 =8---------------Eq II
Solving both equations simaltaneously,
3a^2 +2A^2 =236
4a^2 -2A^2 =16
thus,
a^2=36 cm
Now,
2*36- A^2 =8
A^2=64cm
THUS,
a=6cm ,A=8cm

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harsh dhir   8 years AGO

Let the side of smaller square=a, Area=a^2
Side of Larger Square=A ,Area=A^2

atq,
2a^2-A^2=8 ------ (1)
3a^2+2A^2=236 -----(2)

From (1) & (2),
a=6 cm & A=8 cm

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Rahul Ranjan   8 years AGO

let the side of larger sq. be B and the area of smaller sq. be A.
then, from the question,
we have,
2(A)^2-(B)^2=8 .....(1st eq.)
and
3(A)^2+2(B)^2=236 ....(2nd eq.)
after solving the 1st and 2nd eq.
we got
A=6, B=8

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Meenakshi   8 years AGO

Let Area of Larger square be A and Area of smaller square be B
2B - A = 8 cm^2
3B + 2A=236 cm^2
by solving this equations
B = 36 and A =64
Area of Square = a^2
So, Side of smaller square = 6 cm
and Side of Larger square = 8 cm
Answer is option 6)

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Arka Bhattacharjee   8 years AGO

Let x be the side of the larger square & y the smaller square
2y^2-x^2=8------(1)
3y^2+2x^2=236-----(2)
solving both the equations we get y=6 & x=8

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Kunal nemu   8 years AGO

let x is the side of larger square and y is the side of smaller square.
given 2*y^2 - x^2=8
and 3*y^2 + 2*x^2 = 236
then we get this two equation x=8 and y=6..so the answer is option 6) 6 cm ,8 cm

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B NEHRU KUMARI   8 years AGO

Let area of smaller square=A^2
area of larger square=a^2
Given that
2A^2-a^2=8
3A^2+2a^2=236
Solve then two equation
we will get
Smaller square side A=6cm
larger square side a=8cm

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Chaitanya Singh   8 years AGO

x -> Larger Sqare side
y -> Smaller Sqare side

x*x + 8 = 2*(y*y) AND 3*(y*y) + 2(x*x) = 236

Solving these two we get

x = 8 , y = 6

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anil kumar   8 years AGO

2a^2 - b^2=8
3a^2-2b^2=236
solving above eqns
a=6, b=8

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KODEISWARAN ELANGOVAN   8 years AGO

2a-A=8
3a+2A=236
a=36cm2
side of a=6cm
A=64cm2
side of A=8cm

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Shobha   8 years AGO

2S-L=8cm^2
3S+2L=236cm^2
solving these two equations -
S=36cm^2
L=64cm^2
side of small square =6cm
side of small square =8cm

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pradeep kumar   8 years AGO

let assume area of smaller square =s
and area of larger square =L
so the equations will be
2s-L=8cm^2
3s+2L=236cm^2
after solving we will get 7s=252
s=36
so side of smaller square is 6cm
simmiler side of larger square is 8cm

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