Is a triangle with sides 10, 24, 27 a right triangle

Step by step

The question

Question: find out if a triangle with sides 10, 24, 27 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 27.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 27, the longest side.

2 Square the short sides

Now put the numbers in: a = 10 and b = 24.

10² means 10 times 10.

That is 100.

24² means 24 times 24.

That is 576.

Write the squares.

100 plus 576 is 676.

So a² + b² is 676.

3 Square the longest side

Now put the numbers in: c = 27.

27² means 27 times 27.

That is 729.

So c² is 729.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 676.

c² is 729.

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.