Is a triangle with sides 1.5, 2, 2.5 a right triangle

Step by step

The question

Question: find out if a triangle with sides 1.5, 2, 2.5 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 2.5.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 2.5, the longest side.

2 Square the short sides

Now put the numbers in: a = 1.5 and b = 2.

1.5² means 1.5 times 1.5.

That is 2.25.

2² means 2 times 2.

That is 4.

Write the squares.

2.25 plus 4 is 6.25.

So a² + b² is 6.25.

3 Square the longest side

Now put the numbers in: c = 2.5.

2.5² means 2.5 times 2.5.

That is 6.25.

So c² is 6.25.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 6.25.

c² is 6.25.

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.