Question

A yard is enclosed by a fence that forms a rectangular area. The length of the fences is 7 more than the width. a) Write a polynomial that represents the area by the fence.b) Find the area when the width is 9 yards.

Answer 1

`\begin{gathered} a)\text{Area}_(rec\tan gle)=W^2+7W \\ b)\text{Area}=144yd^2 \end{gathered}`

Step-by-step explanation

Step 1

Graph

The length of the fences is 7 more than the width. ,so

Length= Width+7

replacing

`L=W+7\text{ Equation (1)}`

Step 2

a) Write a polynomial that represents the area by the fence.

the area of a rectangle is given by:

`\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}`

Step 3

b) Find the area when the width is 9 yards.​

replace the value of W in the equation of the area.

`\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}`

I hope this helps you