Is a triangle with sides 2, 3, 4 a right triangle

Step by step

The question

Question: find out if a triangle with sides 2, 3, 4 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 4.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 4, the longest side.

2 Square the short sides

Now put the numbers in: a = 2 and b = 3.

2² means 2 times 2.

That is 4.

3² means 3 times 3.

That is 9.

Write the squares.

4 plus 9 is 13.

So a² + b² is 13.

3 Square the longest side

Now put the numbers in: c = 4.

4² means 4 times 4.

That is 16.

So c² is 16.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 13.

c² is 16.

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.