Question

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?

• A. 84 cm
• B. 74 cm
• C. 78 cm
• D. 76 cm

Answer 1

Answer:

C. 78 cm

Solution: 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: According to the question, Area of Square = Area of Rectangle ⇒ 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) Perimeter of the Rectangle = 2 × (27 + 12) = 78 cm ∴ The correct answer is 78 cm.