Chapter 7, Problem 11PT

To determine

To find: The perimeter of $\Delta ABC$ .

Answer to Problem 11PT

The perimeter of $\Delta ABC$ is $P=16x+h$ .

Explanation of Solution

Given information:

The given information is: $\overline{DE}$ is mid segement having length $m=4x$ , hypotenuse is $h$ .

Calculation:

Since Triangle is isosceles, it’s both side are the same.

Let’s its side are $\left(a,a,h\right)$ .

A midsegement length of a triangle is half of the parallel bottom side of the triangle:

  $a=2m$

Perimeter of the triangle is $P$ .

  $P=a+a+h$

Substitute the value of $a=2m$ and $m=4x$ .

  $\begin{array}{l}P=2m+2m+h\\ P=2\times 4x+2\times 4x+h\\ P=16x+h\end{array}$

Therefore, the perimeter of $\Delta ABC$ is $P=16x+h$ .