Chapter 11.5, Problem 8PSA

To determine

To calculate : The side length of the equilateral triangle with area equal to $9\sqrt{3}{\text{ km}}^2$

Answer to Problem 8PSA

The side length $(a)=6\text{ km}$

Explanation of Solution

Given information : The area of the equilateral triangle is, $A=9\sqrt{3}{\text{ km}}^2$

Formula used : Thearea of an equilateral triangle is as follows:

  $A=\frac{\sqrt{3}}{4}{a}^2$

Where

“ a ” is the side of the equilateral triangle.

Calculation : The area of the triangle is

  $A=\frac{\sqrt{3}}{4}{a}^2$

Substituting the value of $A=9\sqrt{3}{\text{ km}}^2$ in the equation, we get

  $\begin{array}{l}$ 9\sqrt{3}=\frac{\sqrt{3}}{4}{(a)}^2$a^2=36\\ a=6\text{ km}\end{array}$

Thus, we get

  $a=6\text{ km}$