Explanation
Step 1
Graph
The length of the fences is 7 more than the width. ,so
Length= Width+7
replacing
[tex]L=W+7\text{ Equation (1)}[/tex]Step 2
a) Write a polynomial that represents the area by the fence.
the area of a rectangle is given by:
[tex]\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{replacing} \\ \text{Area}_{rec\tan gle}=length\cdot width \\ now,\text{ write length in terms of w usign equation (1)} \\ \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{rec\tan gle}=L\cdot W \\ \text{Area}_{rec\tan gle}=(W+7)\cdot W \\ \text{Area}_{rec\tan gle}=W^2+7W \end{gathered}[/tex]Step 3
b) Find the area when the width is 9 yards.
replace the value of W in the equation of the area.
[tex]\begin{gathered} \text{Area}_{rec\tan gle}=W^2+7W \\ \text{Area}_{rec\tan gle}=(9yd)^2+7(9\text{ yd)} \\ \text{Area}_{rec\tan gle}=81yd^2+63yd \\ \text{Area}=144yd^2 \end{gathered}[/tex]I hope this helps you
