Question

The area of a rectangle having sides in the ratio 1 : 4 is equal to the area of a square of side 8 cm. The perimeter of the rectangle (in cm) is:

• A. 32
• B. 36
• C. 40
• D. 44

Hint:

When dealing with problems involving areas and ratios, start by equating the areas, then solve for the unknowns before calculating other properties like perimeter.

Answer 1

The Correct Option is C

We are given that the sides of the rectangle are in the ratio of 1 : 4. Let the length of the rectangle be \( x \) and the breadth be \( 4x \). The area of the rectangle is given by: \[ \text{Area of rectangle} = x \times 4x = 4x^2 \] The area of the square is: \[ \text{Area of square} = 8 \times 8 = 64 \, \text{cm}^2 \] Equating the areas of the rectangle and the square: \[ 4x^2 = 64 \] Solving for \( x \): \[ x^2 = 16 \quad \Rightarrow \quad x = 4 \, \text{cm} \] Thus, the length of the rectangle is 4 cm, and the breadth is \( 4x = 16 \, \text{cm} \). The perimeter of the rectangle is: \[ \text{Perimeter} = 2 \times (x + 4x) = 2 \times (4 + 16) = 2 \times 20 = 40 \, \text{cm} \] Thus, the correct answer is \( \boxed{40} \).