Is a triangle with sides 25, 7, 24 a right triangle

Step by step

The question

Question: find out if a triangle with sides 25, 7, 24 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 25.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 25, the longest side.

2 Square the short sides

Now put the numbers in: a = 7 and b = 24.

7² means 7 times 7.

That is 49.

24² means 24 times 24.

That is 576.

Write the squares.

49 plus 576 is 625.

So a² + b² is 625.

3 Square the longest side

Now put the numbers in: c = 25.

25² means 25 times 25.

That is 625.

So c² is 625.

Careful!

c is the longest side, 25.

Not the last number we read.

4 Compare

a² + b² is 625.

c² is 625.

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.