Question

is it possible to design a rectangular mango grave whose length is twice its breadth and the area is 800m square? if so,find its lenght and breadth​

Answer 1

Let the breadth of the rectangular mango field be x m.

Then, the length of the rectangular mango field will be 2(x) = 2x m.

Area = 800 m².

Area = length*breadth.

800 = 2x*x

800 = 2x²

2x² - 800 = 0

This is a quadratic equation of the form ax² + bx + c = 0 where a = 2 , b = 0 and c = -800.

If such a rectangular mango field is possible to be designed, then:

b² - 4ac should be greater than or equal to 0 [ b² - 4ac >= 0 ]

b² - 4ac:

= 0² - 4(2)(-800)

= -8(-800)

=6400.

So, it is confirmed that such a rectangular mango field can be designed.

Finding the roots of the equation by using the quadratic formula:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

We already know the value of b²-4ac.

Substituting it in the equation:

$x = \frac{0 \pm \sqrt{6400}}{2(2)} \\ \\ x = \frac{0 \pm 80}{4} \\ \\ x = \frac{80}{4} \\ \\ x = 20 m \\ \\ 2x = 2(20) = 40 m$

Therefore, the length of the rectangular mango field is 40 m and the breadth of it is 20 m.