3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.

Let the breadth of mango grove be l. Length of mango grove will be 2l. Area of mango grove = (2l) (l)= 2l2 2l2 = 800 l2 = 800/2 = 400 l2 – 400 =0 Comparing the given equation with ax2 + bx + c = 0, we get a = 1, b = 0, c = 400 As we know, Discriminant = b2 – 4ac => (0)2 – 4 × (1) × ( – 400) = 1600 Here, b2 – 4ac > 0 Thus, the equation will have real roots. And hence, the desired rectangular mango grove can be designed. l = ±20 As we know, the value of length cannot be negative. Therefore, breadth of mango grove = 20 m Length of mango grove = 2 × 20 = 40 m