Question

A fence is used to enclose a small section of a courtyard. If you have 40 meters of fencing to use, what is the maximum area of the fenced in section?

Answer 1

The maximum area is the highest possible area of the fence

The maximum area is 100 squared units

The perimeter is given as:

$P = 40$

This is calculated as:

$P=2 \times (L + W)$

So, we have:

$2 \times (L + W) =40$

Divide both sides by 2

$L + W =20$

Make L the subject

$L =20 -W$

The area of the fence is:

$A = L \times W$

So, we have:

$A = (20 -W) \times W$

$A = 20W -W^2$

Differentiate

$A' = 20 -2W$

Set to 0

$20 -2W = 0$

Solve for W

$2W = 20$

$W = \frac{20}{2}$

$W = 10$

Recall that:

$A = (20 -W) \times W$

$A = (20 -10) \times 10$

$A = (20 =10) \times 10$

$A = 100$

Hence, the maximum area is 100 squared units

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