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The area of a square and a rectangle are equal. The length of the rectangle is greater than the side of square by 9 cm and its breadth is less than the side of square by 6 cm. What will be the perimeter of the rectangle?

The area of a square and a rectangle are equal. The length of the rectangle is greater than the side of square by 9 cm and its breadth is less than the side of square by 6 cm. What will be the perimeter of the rectangle? Correct Answer 78 cm

Given:

Let a be the side of square, l be the length and b be the breadth of the rectangle

The area of a square and a rectangle are equal ⇒ a2 = l × b

The length of the rectangle is greater than the side of square by 9 cm and its breadth is less than the side of square by 6 cm

l = a + 9

b = a – 6

Formula used:

Area of Square = side2

Area of Rectangle = length × breadth

Perimeter of Rectangle = 2 × (length + breadth)

Calculation:

a2 = l × b

a2 = (a + 9) × (a – 6)

⇒ a2 = a2 – 6a + 9a – 54

⇒ 3a = 54

⇒ a = 18

⇒ l = 18 + 9 = 27 and b = 18 – 6 = 12

⇒ Perimeter of the Rectangle = 2 × (length + breadth)

∴ P = 2 × (27 + 12) = 78 cm

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