Chapter 12.3, Problem 28HP

To determine

Find the length of the altitude of the triangle.

Answer to Problem 28HP

  $\left(d\right)7.5\sqrt{3}$

Explanation of Solution

Given information:

The perimeter of an equilateral triangle is $45$ .

  $\left(a\right)9\left(b\right)9\sqrt{3}\left(c\right)7.5\left(d\right)7.5\sqrt{3}$

Calculation:

Here, we have to find the length of the altitude of the triangle.

As, we know that all the sides of equilateral triangle are equal. Let us suppose the side of the triangle is $a$ . Thus, the altitude will be:

  $h=\frac{\sqrt{3}}{2}a$

Now, the perimeter of the triangle will be:

  $P=3a$

Now, we are given perimeter as $45$ :

  $\begin{array}{l}45=3a\\ a=15\\ h=\frac{\sqrt{3}}{2}a\\ h=\frac{\sqrt{3}}{2}\times 15\\ h=7.5\sqrt{3}\end{array}$

Hence, correct option is $option\left(d\right)$ .