Question

Sum of the areas of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of two squares.

Answer 1

Area of a square = s² 

Perimeter of a square = 4s 

Let the sides of the square be a and b respectively. 

Given, sum of the areas of two squares is 400 cm² and the difference of their perimeters is 16 cm. 

⇒ a² + b² = 400 and 4a – 4b = 16 

⇒ a – b = 4 

⇒ a = 4 + b 

⇒ (4 + b)² + b² = 400 

⇒ 2b² + 8b + 16 = 400 

⇒ b² + 4b – 192 = 0 

⇒ b² + 16b – 12b – 192 = 0 

⇒ (b + 16)(b – 12 ) = 0 

⇒ b = 12 m 

Thus, a = 16 m