Question

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 \(m^2\)? If so, find its length and breadth.

Answer 1

Let the breadth of the mango grove be \(l\). The length of the mango grove will be \(2l\). The area of the mango grove is 800 square meters. This leads to the equation \((2l) (l) = 800\), which simplifies to \(2l^2 = 800\). Further simplification yields \(l^2 = \frac{800}{2}=400\), and then \(l^2-400=0\).

Comparing this equation with the standard quadratic form \(al^2 + bl + c = 0\), we identify the coefficients: a = 1, b = 0, and c = -400.

The discriminant is calculated as \(\Delta = b^2 − 4ac = (0)^2 − 4 \times (1) \times (− 400) = 1600\). Since the discriminant (\(\Delta>0\)), the equation has real roots, indicating that a rectangular mango grove with these specifications is feasible.

The solutions for \(l\) are \(l= ±20\). As length cannot be negative, we consider the positive value.

Therefore, the breadth of the mango grove is 20 m, and the length of the mango grove is \(2 \times 20 = 40\) m.