Question

What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 3 and 9?

Answer 1

The length of the hypotenuse is `3sqrt3` units

Explanation:

Using pythagoras theorem, which is `a^2+b^2=c^2` where c is the longest side (it is the side OPPOSITE to the right angle) and a,b are the other two sides of the triangle. Also, pythagoras theorem only works for triangles with a right angle

`3^2+9^2=c^2`
`9+18=c^2`
`c^2=27`
`c=+-sqrt27`

Now since c is a length, `c>0`
therefore, `c=sqrt27=3sqrt3` only