Is a triangle with sides 12, 9, 16 a right triangle

Step by step

The question

Question: find out if a triangle with sides 12, 9, 16 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 16.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 16, the longest side.

2 Square the short sides

Now put the numbers in: a = 12 and b = 9.

12² means 12 times 12.

That is 144.

9² means 9 times 9.

That is 81.

Write the squares.

144 plus 81 is 225.

So a² + b² is 225.

3 Square the longest side

Now put the numbers in: c = 16.

16² means 16 times 16.

That is 256.

So c² is 256.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 225.

c² is 256.

They are not the same.

So no: it is not a right triangle.

c² is bigger.

So the angle across from c is wider than a right angle.

Let's look back.

First: find the longest side.

Then: square the short sides.

Then: square the longest side.

Last: compare.