Chapter 1, Problem 86RE

To determine

Find the dimensions of each plot.

Answer to Problem 86RE

  $10\times 8feet$

Explanation of Solution

Given information:

A homeowner wishes to fence in three adjoining garden plots, for her children according to the figure. The area of each plot is $80squarefeet$ . She has $88feet$ 88 ft of fencing material.

  

Calculation:

Consider the given figure,

  

The length and width of plot be taken as fence size,

The equation for fencing would be,

  $\begin{array}{l}4w+2l=\mathrm{88.....}\left(1\right)\\ \frac{wl}{3}=\mathrm{80.....}\left(2\right)\\ fromequation\left(2\right)\\ \frac{wl}{3}=80\\ wl=240\\ l=240/w\\ nowsubstitutel=240/wine{q}^n\left(1\right)\\ 4w+2\left(240/w\right)=88\\ 4w+\frac{480}{w}-88=0\\ 4w^2-88w+480=0\\ w^2-22w+120=0\end{array}$

Now we got quadratic equation now solve for width,

  $\begin{array}{l}w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{22\pm \sqrt{-{22}^2-4\times 1\times 120}}{2\times 1}\\ =\frac{22\pm \sqrt{484-480}}{2}\\ =\frac{22\pm \sqrt{4}}{2}\\ =\frac{22\pm 2}{2}\\ =11\pm 1\\ =10,12\end{array}$

Let choose

  $\begin{array}{l}w=10putinwl=240\\ 10l=240\\ l=24\end{array}$

The individual plot is one third in length of total length,

Hence, the dimensions of each plot will be $10\times 8feet$