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Area of a square is 65 sq. cm. Perimeter of a rectangle is equal to the perimeter of this square. Find the length of the rectangle if its breadth is 6.5 cm. Which figure has greater area?

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Area of square = 64 sq.m 

∴ Area = side × side = (side)

⇒ Side = √area = √64 = √82 = 8 

Thus, side is 8 cm. 

then, its perimeter= 4 × side = 4 × 8 = 32 cm 

breadth of rectangle = 6.5 cm and l = a cm 

then perimeter = 2 (6.5 + a) cm

According to question, both perimeter are equal 

∴ 2 (6.5 + a) = 32 

⇒ 6.5 + a = 16 

⇒ a = 16 – 6.5 = 9.5 cm 

Area = l × b = 9.5 × 6.5 = 61.75 sq. cm 

∵ 64 > 61.75 

Thus, length of rectangle = 9.5 cm 

Area of square will be more by 2.25 sq. cm.

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