Question

A rectangular garden has a perimeter of 100 meters and an area of 600 m². What is the length of the garden?

• A. 20 m
• B. 30 m
• C. 40 m
• D. 50 m

Hint:

For rectangle problems with perimeter and area, form a quadratic equation using $L + W$ and $L \cdot W$.

Answer 1

The Correct Option is B

- Step 1: Let length = $L$ and width = $W$. Given perimeter $2(L + W) = 100$, so $L + W = 50$. Area $L \cdot W = 600$.
- Step 2: From $L + W = 50$, express $W = 50 - L$. Substitute into area: $L(50 - L) = 600$.
- Step 3: Form quadratic: $L^2 - 50L + 600 = 0$.
- Step 4: Solve: Discriminant = $50^2 - 4 \cdot 600 = 2500 - 2400 = 100$. Roots: $L = \dfrac{50 \pm \sqrt{100}}{2} = 30$ or $20$.
- Step 5: If $L = 30$, $W = 50 - 30 = 20$. Area = $30 \times 20 = 600$, perimeter = $2(30 + 20) = 100$. Matches.
- Step 6: Check options: Option (b) is 30 m, which matches.