Chapter 7.1, Problem 16PPS

To determine

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

Answer to Problem 16PPS

The measure of shortest side of the triangle is $7\text{cm}$ .

Explanation of Solution

The perimeter of a triangle is given by,

  $\begin{array}{c}\frac{1}{4}x+\frac{1}{3}x+\frac{1}{6}x=31.5\\ \frac{3}{4}x=31.5\\ x=\frac{31.5\times 4}{3}\\ x=42\end{array}$

The sides of the triangle are:

  $\begin{array}{c}\frac{1}{4}\left(x\right)=\frac{1}{4}\left(42\right)\\ =10.5\text{cm}\end{array}$

And,

  $\begin{array}{c}\frac{1}{3}\left(x\right)=\frac{1}{3}\left(42\right)\\ =14\text{cm}\end{array}$

Also,

  $\begin{array}{c}\frac{1}{6}\left(x\right)=\frac{1}{6}\left(42\right)\\ =7\text{cm}\end{array}$

Therefore, the measure of shortest side of the triangle is $7\text{cm}$ .