Third side of a triangle with sides 6 and 6

Step by step

The question

Question: what can the third side be, if a triangle has sides 6 and 6?

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 6 plus 6, which is 12.

Else the two sides cannot reach round it.

2 Shortest it can be

And the third side plus 6 must be longer than 6.

So it must be longer than 6 minus 6: 0.

Careful!

The third side can be the longest side.

It only has to be shorter than 12.

So the third side is between 0 and 12, but not 0 or 12 itself.

3 Check

Let's check with a third side of 7, between 0 and 12: 6 plus 6 is 12, more than 7.

6 plus 7 is 13, more than 6.

A triangle works.

So the answer is right!

Let's look back.

First: longest it can be.

Then: shortest it can be.

Last: check.