The perimeter of two squares are 68 cm. Find the perimeter of the third square whose area is equal to the different of the areas of these two squares.

• A. 8 cm
• B. 64 cm
• C. 32 cm
• D. 60 cm

Answer: (C)

a1 = 68/4 = 17 cmand a2 = 60/4 = 15 cm [ where a1 and a2 are sides]According to the question,Area of the third square = [(17)2 - (15)2 ] = (17 + 15) (17 - 15) = 32 x 2 = 64 sq cmLet a3 = Side of the third square.According to the question, (a3)2 = 64 sq cm ? a3 = ?64 = 8 cm? Perimeter of the third square = 4 x a3 = 4 x 8 = 32 cm.