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.