Chapter 7.1, Problem 15PPS

To determine

To find: The measure of longest side of the triangle.

Answer to Problem 15PPS

The measure of longest side of the triangle is $2.2\text{ft}$ .

Explanation of Solution

The perimeter of a triangle is given by,

  $\begin{array}{c}\frac{1}{4}x+\frac{1}{8}x+\frac{1}{6}x=4.75\\ \frac{13}{24}x=4.75\\ x=\frac{4.75\times 24}{13}\\ x=8.8\end{array}$

The sides of the triangle are:

  $\begin{array}{c}\frac{1}{4}\left(x\right)=\frac{1}{4}\left(8.8\right)\\ =2.2\text{ft}\end{array}$

And,

  $\begin{array}{c}\frac{1}{8}\left(x\right)=\frac{1}{8}\left(8.8\right)\\ =1.1\text{ft}\end{array}$

Also,

  $\begin{array}{c}\frac{1}{6}\left(x\right)=\frac{1}{6}\left(8.8\right)\\ =1.47\text{ft}\end{array}$

Therefore, the measure of longest side of the triangle is $2.2\text{ft}$ .