Question

A rectangle has a perimeter of 50 cm and an area of 150 cm². Find its length.

• A. 15 cm
• B. 10 cm
• C. 20 cm
• D. 25 cm

Hint:

For rectangle problems, form a quadratic using perimeter and area equations.

Answer 1

The Correct Option is A

- Step 1: Set up equations. Let length = $l$, width = $w$. Perimeter: $2(l + w) = 50 \implies l + w = 25$. Area: $l \cdot w = 150$.
- Step 2: Form quadratic. $w = 25 - l$. So, $l (25 - l) = 150 \implies 25l - l^2 = 150 \implies l^2 - 25l + 150 = 0$.
- Step 3: Solve. Discriminant: $\Delta = 25^2 - 4 \cdot 150 = 625 - 600 = 25$. Roots:
\[ l = \frac{25 \pm \sqrt{25}}{2} = \frac{25 \pm 5}{2} \implies l = 15 \text{ or } 10. \] - Step 4: Verify. If $l = 15$, $w = 25 - 15 = 10$. Area: $15 \cdot 10 = 150$. If $l = 10$, $w = 15$. Both work.
- Step 5: Select length. Choose $l = 15$.
- Step 6: Conclusion. Option (1) 15 cm is correct.