Chapter 4.8, Problem 24P

To determine

To find the dimensions of the pen.

Answer to Problem 24P

The dimension of the pen is 5m and 11m or 5.5m and 10m.

Explanation of Solution

Given information: A farmer plans to use 21 m of fencing to enclose a rectangular pen having area 55meter square.

Calculation: The required solution is obtained as,

Let $x$ be length, $y$ be width.

Equation for area, $xy=55$ .

Equation for the amount of fencing ,

  $\begin{array}{l}2x+y=21\\ y=21-2x\end{array}$

Substitute $y=21-2x$ into the equation for area.

  $\begin{array}{l}x\left(21-2x\right)=55\\ 21x-2x^2=55\\ 2x^2-21x+55=0\\ 2x^2-10x-11x+55=0\\ 2x\left(x-5\right)-11\left(x-5\right)=0\\ \left(2x-11\right)\left(x-5\right)=0\\ x=5,5.5\end{array}$

If $x=5,y=21-2x=21-2\cdot 5=21-10=11$

If $x=5.5,y=21-2x=21-2\cdot 5.5=21-11=10$

Hence, the dimension of the pen is 5m and 11m or 5.5m and 10m.