Chapter 16, Problem 5RP

To determine

To find: The value of the semi perimeter.

Answer to Problem 5RP

The value of the semi perimeter is $6\text{unit}$ .

Explanation of Solution

Given information:

The ratio of a triangle’s inradius to its circumradius is $4:6\sqrt{2}$ .

The value of the semi perimeter is calculated as by using inradius and circumradius formula,

  $\begin{array}{l}\frac{r}{R}=\frac{\frac{A}{s}}{\frac{abc}{4A}}\\ \frac{r}{R}=\frac{4A^2}{s\left(abc\right)}\\ \frac{4}{6\sqrt{2}}=\frac{4{\left(8\right)}^2}{s\left(6\sqrt{2}\right)}\\ s=6\text{unit}\end{array}$

Thus, the value of the semi perimeter is $6\text{unit}$ .