Question

Mark bought 222 meters of fencing to

enclose an area of pasture for his
sheep. He plans to use all of the fencing
to make a rectangle that is twice as long
as it is wide.
Use the information you have to create a
system of equations. Let - length and
W = width.
Find the length (in meters) of the area he plans
to fence in.
Enter the correct answer.
DONE
+00
DOH
Clear all

Answer 1

Explanation

We are given the following:

`\begin{gathered} \text{ Perimeter of pasture = 222m} \\ \text{ length =2 }*\text{ width} \end{gathered}`

We are required to determine the length of the area he plans to fence.

From the information given, we have:

`\begin{gathered} Perimeter=222 \\ Perimeter=2(l+w) \\ 222=2(l+w) \\ (222)/(2)=(2(l+w))/(2) \\ 111=l+w \\ \therefore l+w=111\text{ \lparen equation 1\rparen} \\ \\ length=2* width \\ l=2w\text{ \lparen equation 2\rparen} \end{gathered}`
`\begin{gathered} \text{ Substitute for ''l'' in equation 1} \\ l+w=111 \\ 2w+w=111 \\ 3w=111 \\ (3w)/(3)=(111)/(3) \\ w=37 \\ \\ From\text{ }l=2w \\ when\text{ }w=37 \\ l=2(37) \\ l=74m \end{gathered}`

Hence, the answer is:

`l=74m`