Question

Sum of the area of two squares is 500 m² . If the difference of their perimeters is 40m, find the sides of the two squares.

Answer 1

Let the side of the squares be x and y meters.

According to the condition,

x² + y² = 500

4x – 4y = 40

(x – y) = 10

y = x – 10

Substituting the value of y in, we get

x² + (x – 10)² – 500

2x² – 20x – 400 = 0

x² – 10x – 200 = 0

x = 20 or x = – 10

As the side cannot be negative, x = 20 

Hence, side of the first square, x = 20 m 

Side of the second square, y = 20 – 10 = 10 m