Question

The area of a rectangle is 4 times the area of a square. The area of the square is 729 cm\(^2\) and the length of the rectangle is 81 cm. What is the difference between the side of the square and the breadth of the rectangle?

• A. 18 cm
• B. 27 cm
• C. 24 cm
• D. 9 cm

Hint:

Use formulas for area and solve stepwise to find missing dimensions.

Answer 1

The Correct Option is D

Step 1: Find the side of the square.
Given area of square = 729 cm\(^2\)
\[ \text{side of square} = \sqrt{729} = 27 \text{ cm} \] Step 2: Find the area of the rectangle.
\[ \text{Area of rectangle} = 4 \times \text{area of square} = 4 \times 729 = 2916 \text{ cm}^2 \] Step 3: Calculate the breadth of the rectangle using length = 81 cm.
\[ \text{Area} = \text{length} \times \text{breadth} \implies \text{breadth} = \frac{2916}{81} = 36 \text{ cm} \] Step 4: Find the difference between side of square and breadth of rectangle.
\[ \text{Difference} = 36 - 27 = 9 \text{ cm} \] Hence, the answer is \(\boxed{9 \text{ cm}}\).