Chapter 7, Problem 13SGR

To determine

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

Answer to Problem 13SGR

The length of longest side is $120\text{in}$

Explanation of Solution

Given information:

The given information is:

The ratio of the lengths of the three sides of triangle $5:8:10$ .

The perimeter of triangle is $276\text{inches}$ .

Calculation:

The expression $a:b:c$ means that the ratio of the first two quantities is $a:b$ the ratio of the last two quantities is $b:c$ and the ratio of the first and last quantities is $a:c$ .

Just as the ratio $\frac{5}{8}$ or $5:8$ is equivalent to $\frac{5x}{8x}$ or $5x:8x$ .

The extended ratio can be written as $5x:8x:10x$ .

The perimeter is $276$ inches, so the sum of the lengths of the sides is $276$ .

Now,

  $\begin{array}{c}5x+8x+10x=276\\ 23x=276\\ x=12\end{array}$

The measures of the three sides are,

  $\begin{array}{c}5x=5\times 12\\ =60\end{array}$

  $\begin{array}{c}8x=8\times 12\\ =96\end{array}$

And

  $\begin{array}{c}10x=10\times 12\\ =120\end{array}$

Therefore, the length of longest side is $120\text{in}$ .