Question

Ok very confused on this problem, can you help me out?

Answer 1

Given the triangle ABC, you need to remember that, by definition:

- The longest side of a triangle is opposite the largest angle of the triangle.

- The shortest side of a triangle is opposite the smallest angle of the triangle.

In this case, you can identify that:

• The largest angle of the triangle is:

$m\angle B=87\text{\degree}$

And the side opposite it is the longest side:

$AC=29$

• The smallest angle is:

$m\angle C=43\text{\degree}$

Since the side opposite to this angle is:

$AB=4x$

You know that this must be the shortest side of the triangle. Therefore, this must be less than 29 and also less than 22. Notice that:

1. If:

$x=10$

Then:

$AB=4(10)=40$

2. If:

$x=6$

Then:

$AB=4(6)=24$

3. If:

$x=5$

Then:

$AB=4(5)=20$

4. If:

$x=7$

Then:

$AB=4(7)=28$

Notice that the only length less than 29 and less than 22, is obtained by substituting this value of "x" into the expression for the side AB:

$x=5$

Hence, the answer is: Third option.