Question

A triangle has the following measurements. What is a possible length for the third side?

AB = 4, BC = 17, CA = ?

a.18

b.5

c.10

d.12

Answer 1

Can't be 5 because of the triangle inequality thm, which says that two sides of a triangle must ALWAYS add up to longer than the third side. Here's why:

This is a situation where the two sides are smaller than the third. It can't close the figure!

Here's a situation where it's the same size. They're just two lines right on top of each other, not a triangle.

So the sum of two sides must always be greater than the third.

5+4 isn't > 17, doesn't work.
10 + 4 isn't > 17, doesn't work
12 + 4 isn't > 17, doesn't work

18 + 4 > 17
4 + 17 > 18
17 + 18 > 4

Works for all pairs of sides, so A. 18 is the answer.

Answer 2

Thank you!