Question

A rectangular plot of land is to be enclosed by a fence. One side is along a river, and does not need to be enclosed. If the total available fencing is 600 meters, find the dimensions of the plot to have the maximum area

Answer 1

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:  $x = \frac{-b}{2a}$

Solving for the value of k similarly, we get:

$k = \frac{-b}{2a} = \frac{600}{2(-2)} = 150$

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.