Is a triangle with sides 20, 21, 29 a right triangle

Step by step

The question

Question: find out if a triangle with sides 20, 21, 29 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 29.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 29, the longest side.

2 Square the short sides

Now put the numbers in: a = 20 and b = 21.

20² means 20 times 20.

That is 400.

21² means 21 times 21.

That is 441.

Write the squares.

400 plus 441 is 841.

So a² + b² is 841.

3 Square the longest side

Now put the numbers in: c = 29.

29² means 29 times 29.

That is 841.

So c² is 841.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 841.

c² is 841.

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.