Chapter 11.6, Problem 37PPE

To determine

To prove that the formula of equilateral triangle represent a direct variation or an inverse variation with perimeter. $p=3s$ .

Answer to Problem 37PPE

The reason is given in last of explanation

Explanation of Solution

Given:

Given equation

  $P=3s$

Calculation:

In order to solve the question we need to firstly show perimeter of equilateral triangle

Perimeter of triangle is as given in question , P=3 ×side

So we consider perimeter is $y$ , and $3$ is $k$ (constant variation) and side $s$ is $x$

  $\begin{array}{l}P=3s\\ Pisyandsisx\\ soas\frac{P}{s}=3\\ \frac{y}{x}=ky\mathrm{<mi>\alpha </mi>}x\end{array}$ ,

So it is a direct variation as we know that in direct variation ( $y\propto x$ )

  $\begin{array}{l}y=kxory\mathrm{<mi>\alpha </mi>}x\\ ork=\frac{y}{x}\end{array}$

Hence proved

Thus, the solution is correct.