Answer:
Width 150 meters.
Length = 350 meters.
Step-by-step explanation:
Let us assume the width of the fence = k meters
So, both sides = k + k = 2k meters
Also, the TOTAL fencing length = 600 m
So, the one side length of the fence = (600 - 2 k) meters
AREA = LENGTH x WIDTH
⇒ A(k) = (600 - 2k) (k)
or, A = -2k² + 600 k
The above equation is of the form: ax² +bx + C
Here: a = - 2 , b = 600 and C = 0
As a< 0, the parabola opens DOWNWARDS.
Here, x value is given as: ![x = \frac{-b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D)
Solving for the value of k similarly, we get:
![k = \frac{-b}{2a} = \frac{600}{2(-2)} = 150](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D%20%20%3D%20%5Cfrac%7B600%7D%7B2%28-2%29%7D%20%20%3D%20150)
Thus the desired width = k = 150 meters
So, the desired dimensions of the plot is width 150 meters.
And length = 650 - 2k = 650 - 300 = 350 meters.