Question

If two sides of a triangle are 9 cm and 15 cm in length, which COULD be the measure of the third side?

Answer 1

There are 2 possible answers to this:

Explanation:

The 9cm for sure is one of the triangle's legs, or one of the short sides, but the 15cm length could be a leg or a hypotenuse

So let's say that the 15 cm one is the hypotenuse, or the longest side of the triangle. We can use the pythagorean theorem of `a^2+b^2=c^2`
Since the 15 cm one is the hypotenuse, that would make it the C value, and the 9 cm one the A or B value, depending on the one you would like. To solve for the missing value, we can do this if A is the 9cm
`9^2+b^2=15^2`
if we were to solve this by isolating the b value: `b^2=15^2-9^2` we would get `b=12 cm`

The other option we had is both the 15 and 9 cm long segments are legs, or the shorter sides. Then to find the long side, or C, we can simply do `9^2+15^2=c^2`, which when solved, we get `c=17.493 cm`