Question:
The area of a rectangle is 63 cm², and its perimeter is 32 cm. What is the length of the rectangle?
The area of a rectangle is 63 cm², and its perimeter is 32 cm. What is the length of the rectangle?
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For rectangle problems, use area and perimeter to form a quadratic equation.
Updated On: Jul 24, 2025
- 7 cm
- 9 cm
- 11 cm
13 cm
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The Correct Option is B
Solution and Explanation
Let length = \( l \), width = \( w \).
Given: \( l \cdot w = 63 \), \( 2(l + w) = 32 \Rightarrow l + w = 16 \).
Solve: \( w = 16 - l \), so \( l (16 - l) = 63 \).
\[ l^2 - 16l + 63 = 0 \] \[ l = \frac{16 \pm \sqrt{256 - 252}}{2} = \frac{16 \pm 2}{2} = 9, 7 \] Length = 9 cm, width = 7 cm.
Thus, the answer is 9 cm.
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