Question

If the twice the area of small square , is subracted from the area or large square, the result is 14 cm² . However, if twice the area of larger square is added to 3 times the area of smaller square, the result is 203 cm². Determine sides of two squares.

Answer 1

Hey!

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Let the area of small square be x cm^2

Case - 1

If twice the area of small square is subtracted from area of larger square, the result will be 14 cm^2

Thus, area of larger sqaure = ( 14 + 2x^2) cm^2

Case - 2

If twice the area of larger square is added to 3 times the area of smaller square, then the result is 203 cm^2

So, A.T.Q

2 ( 14 + 2x^2) + 3x^2 = 203
28 + 4x^2 + 3x^2 = 203
28 + 7 x^2 = 203
7x^2 = 203 - 28
7x^2 = 175
x^2 = 175/7
x^2 = 25
x= √25
x = 5 cm

Thus, sides of small square is 5 cm each.

Now, area of large square = ( 14 + 2 × 5 × 5 )

= 64 cm^2

Side of the larger square = √64
= 8 cm

Thus, sides of larger square is 8 cm each.

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Hope it helps...!!!

Answer 2

Hey !!

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Let a be the side of small square and b be side of large square

Now,

According to the question ,first equation will be

b^2 - 2a^2=14

Second equation will be

2b^2 + 3a^2=203

Solving both the equations

b^2=14 + 2a^2

Put value of b in 2nd equation

2 (14+2a^2) + 3b^2=203

28 + 4a^2 + 3a^2=203

28 + 7a^2=203

7a^2 = 203-28

7a^2 = 175

a^2 = 175/7

a^2 = 25

a = √25

a=5

Put Value of a in first equation

b^2 - 2a^2=14

b^2 = 14 + 2a^2

b^2 = 14 + 2(5)^2

b^2 = 14+50

b^2 = 64

b = √64

b = 8

Hence a=5,b=8

Side of small square is 5cm and side of large square is 8 cm

Hope it is satisfactory :-)

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