Sum of the areas of two squares is 400 cm2. If the difference of their

1.	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» 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

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»

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