Is a triangle with sides 4, 7, 8 a right triangle

Step by step

The question

Question: find out if a triangle with sides 4, 7, 8 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 8.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 8, the longest side.

2 Square the short sides

Now put the numbers in: a = 4 and b = 7.

4² means 4 times 4.

That is 16.

7² means 7 times 7.

That is 49.

Write the squares.

16 plus 49 is 65.

So a² + b² is 65.

3 Square the longest side

Now put the numbers in: c = 8.

8² means 8 times 8.

That is 64.

So c² is 64.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 65.

c² is 64.

They are not the same.

So no: it is not a right triangle.

c² is smaller.

So even the biggest angle is less 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.