Question

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

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

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

hope this helps: