Third side of a triangle with sides 12 and 20

Step by step

The question

Question: what can the third side be, if a triangle has sides 12 and 20?

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 12 plus 20, which is 32.

Else the two sides cannot reach round it.

2 Shortest it can be

And the third side plus 12 must be longer than 20.

So it must be longer than 20 minus 12: 8.

Careful!

The third side can be the longest side.

It only has to be shorter than 32.

So the third side is between 8 and 32, but not 8 or 32 itself.

3 Check

Let's check with a third side of 21, between 8 and 32: 12 plus 20 is 32, more than 21.

12 plus 21 is 33, more than 20.

A triangle works.

So the answer is right!

Let's look back.

First: longest it can be.

Then: shortest it can be.

Last: check.