Chapter 3.7, Problem 20PSB

To determine

To calculate : The perimeter of the triangle ABC.

Answer to Problem 20PSB

The value of perimeter is 77 cm .

Explanation of Solution

Given information : The following information has been given regarding the triangle

A is the vertex of this isosceles triangle

  $m\angle B=2\left|\overrightarrow{BC}\right|$

  $m\angle C=3\left|\overrightarrow{AB}\right|$

  $m\angle B=(x+6)$

  $m\angle C=(2x-54)$

Formula used : Information/data provided in the question that are used to solve this particular category of solution/solution.

Calculation : As we know that A is the vertex of this isosceles triangle, we can say that

  $\angle B\cong \angle C$

So, we can say from the given information that

  $x+6=2x-54\to x=60$

Now, we substitute the value of x in $m\angle B=2\left|\overrightarrow{BC}\right|$ , where $m\angle B=(x+6)$ . Thus, we get

  $x+6=66=2\left|\overrightarrow{BC}\right|\to \left|\overrightarrow{BC}\right|=33$

Now, we substitute the value of x in $m\angle C=3\left|\overrightarrow{AB}\right|$ , where $m\angle C=(2x-54)$ . Thus, we get

  $66=3\left|\overrightarrow{AB}\right|\to \left|\overrightarrow{AB}\right|=22$

Also, ABC being an isosceles triangle, we know that AB and AC are of same measurements. Thus, we can say that perimeter is

  $P=2(22)+33\to 77cm$