Chapter 11.1, Problem 7CYU

To determine

To calculate: The perimeter and area of triangle.

Answer to Problem 7CYU

The area and perimeter of triangle is $33.75in{.}^2$ and $28.5in.$ respectively.

Explanation of Solution

Calculation:

Use the Pythagoras theorem to calculate the height of the triangle.

  $\begin{array}{c}{a}^2+b^2=c^2\\ $ h^2+4^2={(8.5)}^2$$ h^2={(8.5)}^2-4^2$h^2=72.25-16\\ h^2=56.25\\ h=\sqrt{56.25}\\ h=7.5in.\end{array}$

For the area of triangle,

  $\begin{array}{l}\text{Area = }\frac{1}{2}\times \text{base }\times \text{ height}\\ \text{Area}=\frac{1}{2}\times 9\times 7.5\\ \text{Area}=\frac{1}{2}\times 67.5\\ \text{Area}=33.75in{.}^2\end{array}$

Now, for the perimeter of triangle.

  $\begin{array}{l}\text{Perimeter }=9+8.5+11\\ \text{Perimeter }=28.5in.\end{array}$