Is a triangle with sides 11, 60, 61 a right triangle

Step by step

The question

Question: find out if a triangle with sides 11, 60, 61 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 61.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 61, the longest side.

2 Square the short sides

Now put the numbers in: a = 11 and b = 60.

11² means 11 times 11.

That is 121.

60² means 60 times 60.

That is 3600.

Write the squares.

121 plus 3600 is 3721.

So a² + b² is 3721.

3 Square the longest side

Now put the numbers in: c = 61.

61² means 61 times 61.

That is 3721.

So c² is 3721.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 3721.

c² is 3721.

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.