Is a triangle with sides 5, 6, 7 a right triangle

Step by step

The question

Question: find out if a triangle with sides 5, 6, 7 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 7.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 7, the longest side.

2 Square the short sides

Now put the numbers in: a = 5 and b = 6.

5² means 5 times 5.

That is 25.

6² means 6 times 6.

That is 36.

Write the squares.

25 plus 36 is 61.

So a² + b² is 61.

3 Square the longest side

Now put the numbers in: c = 7.

7² means 7 times 7.

That is 49.

So c² is 49.

Careful!

c is always the longest side.

Find it first.

4 Compare

a² + b² is 61.

c² is 49.

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.