Chapter 7.2, Problem 6P

To determine

To find: The dimensions of the rectangular animal pen.

Answer to Problem 6P

The dimension of the rectangular animal pen is 60 m and 20m or 40 m and 30 m.

Explanation of Solution

Given:

The area of the rectangular animal pen = 1200 m².

The length of the fencing of the rectangular animal pen = 100 m

Calculation:

The area of the rectangle is given by

  $\begin{array}{l}A=l\times b\\ \text{Here, }l\text{is the length of the rectangle and }b\text{ is the bredth of the rectangle}\text{.}\end{array}$

The initial area of the rectangle

  $\begin{array}{l}{A}_1=1200{\text{m}}^2\\ 1200=l\times b\end{array}$

The length of the fencing of the rectangular animal pen will be equal to the perimeter of the rectangular animal pen. The fencing is done on 3 sides.

The perimeter of the rectangle is given by

  $\begin{array}{l}P=l+b+b\\ 100=l+2b\\ l+2b=100\end{array}$

Substitute $b=\frac{1200}{l}$ in the above equation.

  $\begin{array}{l}l+2\times \frac{1200}{l}=100\\ l^2-100l+2400=0\\ l^2-60l-40l+2400=0\\ l\left(l-60\right)-40\left(l-60\right)=0\\ \left(l-40\right)\left(l-60\right)=0\\ l=60\\ l=40\end{array}$

And

The breadth of the rectangle

  $\begin{array}{l}b=\frac{1200}{60}=20\\ b=\frac{1200}{40}=30\end{array}$

The dimension of the rectangular animal pen is 60 m and 20m or 40 m and 30 m.

Therefore, the dimension of the rectangular animal pen is 60 m and 20m or 40 m and 30 m.