Chapter 9.4, Problem 6PSA

To determine

To find: The value of side $PM$

Answer to Problem 6PSA

The value of side $PM=2\sqrt{3}$ units

Explanation of Solution

Given information :

The given triangle is an equilateral.

Each side of the triangle is 4 units.

In a given $\Delta PKO$ , we have

  $PK=KO=OP=4\text{ units}$

  $\therefore KM=\frac{1}{2}KO=\frac{1}{2}\times 4=2\text{ units}$

Formula used :

Altitudes bisect the base at right angle

Calculation :

  

By Pythagoras Theorem in $\Delta PMK$ .

  $\begin{array}{l}P{K}^2=P{M}^2+K{M}^2\\ \Rightarrow 4^2=P{M}^2+2^2\\ \Rightarrow P{M}^2=16-4=12\\ \Rightarrow PM=\sqrt{12}=2\sqrt{3}\text{ units}\end{array}$