Question

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

Answer 1

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 A1 + Area of square A2 = 656 ( GIVEN)
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

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 WILL HELP YOU..

Answer 2

Hey!!!!

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a/q

x2+(x+4)2=656

x2+x2+16+8x=656

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+20)(x-16)=0

x=-20     or  x=16

x=16  (x can't be negative)

hence the sides of square are 16 cm and 20 cm.

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