Question

How do you use the Pythagorean Theorem to determine if the three sides are a right triangle: 9 in, 12 in, 15 in?

Answer 1

The three sides 9 in, 12 in, and 15 in do represent a right triangle.

The hypotenuse is the greatest length. So using the Pythagorean theorem, which states `c^2=a^2+b^2`, where c is the length of the hypotenuse of a right triangle (or the diagonal in case of a square or rectangle), and a and b are the other two sides,

`c^2=a^2+b^2` or `("Hypotenuse")^2=("Base")^2+("Height")^2`

`15^2=9^2+12^2` =

`225=81+144` =

`225=225`

Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, this is a right triangle.