Third side of a triangle with sides 7 cm and 3 cm

Step by step

The question

Question: what can the third side be, if a triangle has sides 7 cm and 3 cm?

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 7 plus 3, which is 10.

Else the two sides cannot reach round it.

2 Shortest it can be

And the third side plus 3 must be longer than 7.

So it must be longer than 7 minus 3: 4.

Careful!

The third side can be the longest side.

It only has to be shorter than 10.

So the third side is between 4 and 10, but not 4 or 10 itself.

3 Check

Let's check with a third side of 8, between 4 and 10: 3 plus 7 is 10, more than 8.

3 plus 8 is 11, more than 7.

A triangle works.

So the answer is right!

Let's look back.

First: longest it can be.

Then: shortest it can be.

Last: check.