Chapter 14, Problem 9MPS

To determine

To Find: Theperimeter of the triangle with the area of $3\sqrt{3}$ .

Answer to Problem 9MPS

The perimeter is $6\sqrt{3}$ .

Explanation of Solution

Given:

The area of the equilateral triangle varies directly as the square of the perimeter.

The equilateral with perimeter of 18 has the area of $9\sqrt{3}$ .

Calculation:

Consider the equation for the variable of the area with the perimeter is,

  $a=k{p}^2$

Then

  $\begin{array}{l}9\sqrt{3}=k{18}^2\\ k=\frac{\sqrt{3}}{36}\end{array}$

Thus, the formula is,

  $a=\frac{\sqrt{3}}{36}{p}^2$

The perimeter for the area of $3\sqrt{3}$ is,

  $\begin{array}{l}3\sqrt{3}=\frac{\sqrt{3}}{36}{p}^2\\ p=6\sqrt{3}\end{array}$