Chapter 4.8, Problem 6P

To determine

To find the dimensions of the garden .

Answer to Problem 6P

The solution is $24$ ft and $9$ ft.

Explanation of Solution

Given information: A rectangle garden has perimeter $66$ ft and area $216$ ft square.

Calculation: Dimensions of the garden is obtained as,

Let $x$ is width,

  $y$ is length.

The area of the garden is 216 , $xy=216$

The perimeter of the garden is 66,

  $\begin{array}{l}2x+2y=66\\ 2x=66-2y\\ x=33-y\end{array}$

Substitute $x=33-y$ into the equation for area.

  $\begin{array}{l}\left(33-y\right)y=216\\ 33y-y^2=216\\ y^2-33y+216=0\\ y^2-24y-9y+216=0\\ y\left(y-24\right)-9\left(y-24\right)=0\\ \left(y-9\right)\left(y-24\right)\\ y=9,24\end{array}$

  $x+4=9+4=13$ is length.

If $y=9$ , $x=33-y=33-9=24$

If $y=24$ , $x=33-y=33-24=9$

Hence,the solution is $24$ ft and $9$ ft.