Step by step
The question
Question: find out if a triangle with sides 13, 5, 12 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 the longest side, 13.
Not the last number we read.
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.