Chapter 11.1, Problem 13PPS

To determine

To calculate: To find the perimeter and area of triangle.

Answer to Problem 13PPS

The area and perimeter of the triangle is $129.9m^2$ and $69.88m$ respectively.

Explanation of Solution

Given information: The given figure in question.

Calculation:

Use Pythagoras theorem to find $h$ of the triangle,

  $\begin{array}{c}{a}^2+b^2=c^2\\ h^2+5^2={10}^2\\ h^2={10}^2-5^2\\ h^2=100-25\\ h^2=75\\ h=\sqrt{75}\\ h=8.66m\end{array}$

For area of the triangle,

  $\begin{array}{l}\text{Area =}\frac{1}{2}\times \text{ base }\times \text{ height}\\ \text{Area}=\frac{1}{2}\times 30\times 8.66\\ \text{Area}=\frac{1}{2}\times 259.8\\ \text{Area}=129.9m^2\end{array}$

Use the Pythagorean Theorem to find the length of the third side of the triangle.

  $\begin{array}{l}{a}^2+b^2=c^2\\ $ {30}^2+{(8.66)}^2=c^2$900+75=c^2\\ 975=c^2\\ \sqrt{975}=c\\ 31.22m=c\end{array}$

For perimeter of the triangle,

  $\begin{array}{c}\text{Perimeter }=31.22+8.66+30\\ =69.88m\end{array}$