Is a triangle with sides 2.5, 6, 6.5 a right triangle Step by Step

Step by step

The question

Question: find out if a triangle with sides 2.5, 6, 6.5 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 6.5.

The two shorter sides are a and b.

Every right triangle has a² + b² = c².

So we test it.

So c = 6.5, the longest side.

c = 6.5

2 Square the short sides

Now put the numbers in: a = 2.5 and b = 6.

a² + b² = 2.5² + 6²

2.5² means 2.5 times 2.5.

That is 6.25.

2.5² = 2.5 × 2.5 = 6.25

6² means 6 times 6.

That is 36.

6² = 6 × 6 = 36

Write the squares.

a² + b² = 6.25 + 36

6.25 plus 36 is 42.25.

So a² + b² is 42.25.

a² + b² = 42.25

3 Square the longest side

Now put the numbers in: c = 6.5.

c² = 6.5²

6.5² means 6.5 times 6.5.

That is 42.25.

6.5² = 6.5 × 6.5 = 42.25

So c² is 42.25.

c² = 42.25

Careful!

c is always the longest side.

Find it first.

Careful: c is always the longest side

4 Compare

a² + b² is 42.25.

c² is 42.25.

They are the same!

42.25 = 42.25

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.

= Yes: a right triangle

Let's look back.

First: find the longest side.

Then: square the short sides.

Then: square the longest side.

Last: compare.

Answer