Question

The sum of the areas of two squares is 640 m² . If the difference in their perimeter be 64m, find the sides of the two square

Answer 1

Let the length of the side of the first and the second square be x and y. respectively. 

According to the question:

x² + y² = 640.....(i)

Also

4x - 4y = 64

⇒ x - y = 16

⇒ x = 16 + y

Putting the value of x in (i), we get:

∴ y = 8

(∵Side cannot be negative)

∴ x = 16 + y = 16 + 8 = 24m

Thus, the sides of the squares are 8 m and 24 m.

Answer 2

Let side of first square be x and that of another be y

I^st case

area of square = (side)²

x² + y² =640 --------------------------   (i) 

2nd case

4x -4y =64

-> x-y=16

x=16+y

put value of x in 1

(16+y)²+y²=640

256+y²+32y+y² =640

2y² +32y =384

y²+16y=192

y² + 24y-8y -192=0

y(y+24) -8(y+24)=0

y=8

and x=24