Question

You have 576 feet of fencing to enclose a rectangular plot of land. Find the dimensions of the rectangular plot that would maximize the area. List the smaller number first.

Answer 1

Answer:

The dimension that maximizes area is 144ft by 144ft

Step-by-step explanation:

Given

$P = 576$ -- perimeter

Required

The dimension that gives maximum area

Perimeter is calculated as:

$P= 2 * (L + W)$

So, we have:

$2 * (L + W) = 576$

Divide through by 2

$L + W = 288$

Make L the subject

$L = 288 -W$

Area is calculated as:

$A = L * W$

Substitute $L = 288 -W$

$A = (288 - W) * W$

Open bracket

$A = 288W - W^2$

Differentiate A with respect to W

$A' = 288 - 2W$

Set to 0 to calculate W

$288 - 2W = 0$

Collect like terms

$2W = 288$

Divide by 2

$W = 144$

Recall that:

$L = 288 -W$

$L = 288 - 144$

$L = 144$