Question

Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).

Hint:

Use perimeter formula to express one variable in terms of the other and substitute into area equation.

Answer 1

Let length = \(l\), breadth = \(b\) Perimeter: \[ 2(l + b) = 100 \Rightarrow l + b = 50 \Rightarrow b = 50 - l \] Area: \[ l \times b = 600 \] Substituting: \[ l(50 - l) = 600 \] \[ 50l - l^2 - 600 = 0 \] \[ l^2 - 50l + 600 = 0 \] Quadratic formula: \[ l = \frac{-(-50) \pm \sqrt{2500 - 2400}}{2} = \frac{50 \pm \sqrt{100}}{2} = \frac{50 \pm 10}{2} \] \[ l = 30, \, 20 \] So, length = \(30 \, \text{m}\), breadth = \(20 \, \text{m}\)