Question

In triangle ABC, the side lengths are AB = 13, AC = 21, and BC = x. Write a compound inequality that represents the range of possible values for x.

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Answer 1

There is only 1 solution for the length of BC.

We can calculate it using Pythagorean theorem.

We can conclude that triangle's hypotenuse is AC.

$AC^2=AB^2+BC^2$

If that is the case we are looking for a side BC.

$BC=\sqrt{AC^2-AB^2}$

Now put in the data.

$BC=\sqrt{21^2-13^2}=\sqrt{272}=\sqrt{272}\approx\boxed{16.49}$

Hope this helps.

r3t40