Question

A rectangle has an area of 60 cm² and a perimeter of 32 cm. What is the length if it is greater than the width?

• A. 10 cm
• B. 12 cm
• C. 14 cm
• D. 16 cm

Hint:

Use area and perimeter to form a quadratic equation for rectangle dimensions.

Answer 1

The Correct Option is A

We need the length of the rectangle.
- Step 1: Define: Length = \( l \), width = \( w \). Area: \( l \cdot w = 60 \). Perimeter: \( 2(l + w) = 32 \Rightarrow l + w = 16 \).
- Step 2: Solve: \( w = 16 - l \). Substitute:
\[ l (16 - l) = 60 \Rightarrow l^2 - 16l + 60 = 0 \] - Step 3: Quadratic: \( l = \frac{16 \pm \sqrt{256 - 240}}{2} = \frac{16 \pm 4}{2} = 10, 6 \).
- Step 4: Since \( l>w \), \( l = 10 \), \( w = 6 \).
- Step 5: Options:
- (a) 10: Correct.
Thus, the answer is a.