Question

If a triangle has sides of lengths 5, 8 and 12, it is a right triangle. true or false

Answer 1

False.

Explanation:

To see if these sides can form a right triangle, all we need to do is see if the following equation holds
`a^2+b^2=c^2` where
`c` is the larger measurement.
`a \text{ and } b` it doesn't really matter which you assign as 5 or 8.

So I'm choosing the following
`a=5,b=8,c=12`.

`c` has to be 12 because 12 is the largest.

Now we got to see if
`a^2+b^2=c^2` holds.

That is, we need to see if
`5^2+8^2=12^2` holds.

`5^2+8^2=12^2`

`25+64=144`

`89=144`

That's totally false. 89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.