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?
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?
Updated On: Mar 5, 2025
- 45 sq. cm
- 75 sq. cm
- 100 sq. cm
- 200 sq. cm
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The Correct Option is B
Solution and Explanation
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.
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