Question

is it possible to design a rectangular mango grove whose length is twice it's breadth and the area is 800 square units ? if so find length and breadth.​

Answer 1

Given :-

Length of the rectangle = 2 × Breadth

Area of the rectangle = 800 unit²

To Find :-

Is it possible to design a rectangular mango grove with the following dimensions mentioned.

The length of the rectangle.

The breadth of the rectangle.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

Let the breadth of mango grove be 'l'. Then the length would be '2l'.

By the formula,

$\underline{\boxed{\sf Area=Length \times Breadth}}$

By substituting,

Area of mango grove = (2l) (l)= 2l²

$\sf 2l^{2} = 800$

$\sf l^{2}=\dfrac{800}{2}$

$\sf l^{2}=400$

$\sf l^{2}- 400 =0$

Comparing the given equation with ax² + bx + c = 0,

$\sf a = 1, \ b = 0, \ c = 400$

We know,

Discriminant = b² – 4ac

$\sf \implies (0)^{2} - 4 \times (1) \times ( - 400) = 1600$

Now, here

$\sf b^{2} - 4ac > 0$

The equation will have real roots. Thus, the desired rectangular mango grove can be designed.

$\sf l = \pm 20$

The value of length cannot be negative.

Therefore,

Breadth of mango grove = 20 m

Length of mango grove = 2l

= 2 × 20 = 40 m

Hence, the length and breadth are 40 m and 20 m respectively.