Question

The area of a square and a rectangle is equal. The length of the rectangle is 6 cm more than the side of the square and breadth is 4 cm less than the side of the square. What is the perimeter of the rectangle?

• A. 48 cm
• B. 62 cm
• C. 42 cm
• D. 52 cm

Answer 1

Answer:

D. 52 cm

Solution:

Given:

The area of a square and a rectangle is equal

The length of the rectangle is 6 cm more than the side of the square

The breadth of the rectangle is 4 cm less than the side of the square

Formula Used:

1. Area of Square = a²

2. Area of Rectangle = l × b

3. Perimeter of Rectangle = 2(l + b)

Where, a = side of square, l & b are length & breadth of rectangle respectively

Calculation:

Let the side of square be a

⇒ Length of rectangle = a + 6

⇒ Breadth of rectangle = a - 4

According to the question,

a² = (a + 6)(a - 4)

⇒ a² = a² - 4a + 6a - 24

⇒ 2a = 24

⇒ a = 12

Perimeter of Rectangle = 2[(12 + 6) + (12 - 4)]

⇒ Perimeter of Rectangle = 2(18 + 8) = 52 cm

∴ The perimeter of rectangle is 52 cm.