Question

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm². Find the sides of the squares.

Answer 1

SOLUTION :

Let A1 & A2 be two squares .  

Given : side of square A1= x cm

side of square A2 =( x + 4 ) cm

Area of square A1 = side × side = x× x= x²

Area of square A2 = side × side  

= (x + 4) (x + 4) = (x + 4)² =  x² + 8x +16

[(a+b)² = a² +2ab +b²]

Area of square A2 = x² + 8x +16

GIVEN : Area of square A1 + Area of square A2 = 656

x² + (x² + 8x +16) = 656

2x² + 8x +16 = 656

2x² + 8x = 656 -16

2x² + 8x = 640

2x² + 8x - 640 = 0

2(x² + 4x -320) = 0

x² + 4x - 320 = 0

x² + 20x -16x - 320 = 0

x( x +20) - 16(x +20) = 0

(x- 16)(x + 20) = 0

(x - 16) = 0  or  (x + 20) = 0

x = 16   or   x  = -20

since, the length of the side of a square cannot be negative. Therefore x = 16 .

Side of square A1= x cm = 16 cm

Side of square A2 = ( x +4 ) cm = 16 + 4 = 20 cm

Hence, side of square A1= 16 cm & side of square A2 = 20 cm.

HOPE THIS  ANSWER WILL HELP YOU..

Answer 2

Solution :

It is given that ,

Side of a first square = x cm,


Side of a second square = ( x + 4 )cm

According to the problem given,

Sum of the areas of the squares = 656cm²

=> x² + ( x + 4 )² = 656 cm²

=> x² + x² + 8x + 16 - 656 = 0

=> 2x² + 8x - 640 = 0

Divide each term by 2 , we get

x² + 4x - 320 = 0

Splitting the middle term , we get

=> x² - 20x + 16x - 320 = 0

=> x( x - 20 ) + 16( x - 20 ) = 0

=> ( x - 20 )( x + 16 ) = 0

=> x - 20 = 0 or x + 16 = 0

=> x = 20 or x = -16

x should not be negative.

Therefore ,

Side of the first square = x = 20 cm

Side of the second square = ( x + 4 )

= 20 + 4

= 24 cm

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