Is a triangle with sides 4, 5, 6 a right triangle

Step by step

The question

Question: find out if a triangle with sides 4, 5, 6 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 6.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 6, the longest side.

2 Square the short sides

Now put the numbers in: a = 4 and b = 5.

4² means 4 times 4.

That is 16.

5² means 5 times 5.

That is 25.

Write the squares.

16 plus 25 is 41.

So a² + b² is 41.

3 Square the longest side

Now put the numbers in: c = 6.

6² means 6 times 6.

That is 36.

So c² is 36.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 41.

c² is 36.

They are not the same.

So no: it is not a right triangle.

c² is smaller.

So even the biggest angle is less 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.