Chapter 8.3, Problem 46HP

To determine

To identify:

Correct value of $x$ from given two equations.

Answer to Problem 46HP

Correct value of $x$ is, $x=3\sqrt{3}$ .

Explanation of Solution

Given information:

Equation:

Carmen Audrey

  $\begin{array}{l}x=\frac{6\sqrt{3}}{2}\\ x=3\sqrt{3}\end{array}$$\begin{array}{l}x=\frac{6\sqrt{2}}{2}\\ x=3\sqrt{2}\end{array}$

  

From the given diagram of triangle is equiangular, the altitude divides the triangle into two smaller congruent $30°-60°-90°$ triangles.

In a $30°-60°-90°$ triangle, the length of the hypotenuse $h$ is $2$ times the length of the shorter leg $s$ , and the length of the longer leg $l$ is $\sqrt{3}$ times the length of the shorter leg.

Theorem of $30°-60°-90°$ , triangle shows that,

  $\begin{array}{l}h=2s\\ 6=2s\\ \frac{6}{2}=s\\ 3=s\end{array}$

And

  $\begin{array}{l}l=\sqrt{3}s\\ x=\sqrt{3}\left(3\right)\\ x=3\sqrt{3}\end{array}$

Therefore, Carmen’s answer is correct.