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.
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