Chapter 8.6, Problem 54HP

To determine

To explain:

The following condition is correct or not:

Answer to Problem 54HP

This condition is not correct.

Explanation of Solution

Given information:

  

The theorem of triangle angle sum for the third angle:

The third angle:

  $180-64-64=52$

Let,

  $x$ : The length of the base of isosceles triangle.

  

If $\Delta ABC$ has length $a$ , $b$ and $c$ representing the length of sides opposite angles with measure $A$ , $B$ and $C$ :

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\mathrm{...}\left(1\right)$

Put the values in equation (1):

  $\frac{\sin {64}^{\circ }}{5}=\frac{\sin {52}^{\circ }}{x}$

Use property of cross product:

  $\begin{array}{l}x\sin {64}^{\circ }=5\sin {52}^{\circ }\\ x=\frac{5\sin {52}^{\circ }}{\sin {64}^{\circ }}\\ x=4.4\end{array}$

The perimeter of the triangle:

  $\begin{array}{l}P=5+5+4.4\\ P=14.4\end{array}$

Therefore, neither of them is correct.