Chapter 13.5, Problem 4PSA

To determine

To find:The perimeter of the triangle.

Answer to Problem 4PSA

The perimeter of the triangle is 43.2.

Explanation of Solution

Given:

The vertices is given as,

  $\left[0,0,6\right],\left[0,8,0\right]\text{ and }\left[15,0,0\right]$

Calculation:

Calculate the value of $S_1$ .

  $\begin{array}{c}{S}_1=\sqrt{8^2+{\left(-6\right)}^2}\\ =\sqrt{100}\\ =10\end{array}$

Calculate the value of $S_2$ .

  $\begin{array}{c}{S}_2=\sqrt{{15}^2+{\left(-8\right)}^2}\\ =\sqrt{289}\\ =17\end{array}$

Calculate the value of $S_3$ .

  $\begin{array}{c}{S}_3=\sqrt{{15}^2+{\left(-6\right)}^2}\\ =\sqrt{261}\\ =16.2\end{array}$

Calculate the perimeter.

  $\begin{array}{c}P=S_1+S_2+S_3\\ =10+17+16.2\\ =43.2\end{array}$

Thus, the perimeter of the triangle is 43.2.