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

Jun 5, 2015

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 ${\left(\text{Hypotenuse")^2=("Base")^2+("Height}\right)}^{2}$

${15}^{2} = {9}^{2} + {12}^{2}$ =

$225 = 81 + 144$ =

$225 = 225$

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