Question

Perimeter of a rectangle is equal to the perimeter of a square whose diagonal is \(10\sqrt2\) cm. If the length of the rectangle is thrice its breadth, then what is the area of the rectangle?

• A. 45 sq. cm
• B. 75 sq. cm
• C. 100 sq. cm
• D. 200 sq. cm

Answer 1

The Correct Option is B

Step 1: Find the side and perimeter of the square

The diagonal of the square is \( 10\sqrt{2} \) cm. 

The side of the square is:

\( \text{Side} = \frac{\text{Diagonal}}{\sqrt{2}} = \frac{10\sqrt{2}}{\sqrt{2}} = 10 \) cm.

The perimeter of the square is:

\( 4 \times 10 = 40 \) cm.

Step 2: Find the dimensions of the rectangle

The perimeter of the rectangle is also 40 cm. Let:

• Length = \( 3x \)
• Breadth = \( x \)

The perimeter equation is:

\( 2(3x + x) = 40 \) \( \Rightarrow 8x = 40 \) \( \Rightarrow x = 5 \).

Step 3: Calculate the area of the rectangle

\( \text{Area} = \text{Length} \times \text{Breadth} = 3x \times x = 3 \times 5 \times 5 = 75 \) sq. cm.

Conclusion:

The area of the rectangle is 75 sq. cm.