Question 30

Explanation

A piece of land will be bordered by a fence using barbed wire

Determining Variables

Let the length of the land area $= x$ and the width of the land area $= y$

Wire Constraint

Notice the fence shape consists of $4$ layers. This means

Therefore, the fenced land can be expressed as

Area Function

If the land area $= xy$, then

Maximum Area

To find the maximum area, differentiate $L$ with respect to $y$ and set it equal to $0$

Substitute $y = 50$ into the area function

Therefore, the maximum area of the fenced land (in $\text{m}^2$) is $5{,}000 \text{ m}^2$