Question

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.​

Answer 1

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Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove = (2l) (l)= 2l^2

2l^2 = 800

l^2 = 800/2 = 400

l^2 – 400 =0

Comparing the given equation

with ax^2 + bx + c = 0, we get

a = 1, b = 0, c = 400

As we know, Discriminant = b^2 – 4ac

=> (0)^2 – 4 × (1) × ( – 400) = 1600

Here, b^2 – 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

Answer 2

yes it is possible.

let breadth=x

length=2x

area=2x²

according to ques.

2x²=800

x²=400

x=20

Hence, Length=40

Breadth=20