Is a triangle with sides 5, 12, 13 a right triangle

Step by step

The question

Question: find out if a triangle with sides 5, 12, 13 is a right triangle.

1 Find the longest side

In a right triangle, the longest side is across from the right angle.

We call it c.

Here it is 13.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 13, the longest side.

2 Square the short sides

Now put the numbers in: a = 5 and b = 12.

5² means 5 times 5.

That is 25.

12² means 12 times 12.

That is 144.

Write the squares.

25 plus 144 is 169.

So a² + b² is 169.

3 Square the longest side

Now put the numbers in: c = 13.

13² means 13 times 13.

That is 169.

So c² is 169.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 169.

c² is 169.

They are the same!

The rule a² + b² = c² works only in right triangles.

So the angle across from c is a right angle.

So yes: it is a right triangle.

Let's look back.

First: find the longest side.

Then: square the short sides.

Then: square the longest side.

Last: compare.