Question

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

Answer 1

Answer:

False.

Step-by-step 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.