Third side of a triangle with sides 5 and 9

Step by step

The question

Question: what can the third side be, if a triangle has sides 5 and 9?

In a triangle, any two sides together are longer than the third side.

1 Longest it can be

The third side must be shorter than 5 plus 9, which is 14.

Else the two sides cannot reach round it.

2 Shortest it can be

And the third side plus 5 must be longer than 9.

So it must be longer than 9 minus 5: 4.

Careful!

The third side can be the longest side.

It only has to be shorter than 14.

So the third side is between 4 and 14, but not 4 or 14 itself.

3 Check

Let's check with a third side of 10, between 4 and 14: 5 plus 9 is 14, more than 10.

5 plus 10 is 15, more than 9.

A triangle works.

So the answer is right!

Let's look back.

First: longest it can be.

Then: shortest it can be.

Last: check.