The hypotenuse of a right triangle can be calculated using the Pythagorean Theorem. This theorem states that if we know the lengths of the two other legs of the triangle, then we can calculate the hypotenuse. It is written in the following way:

In this formula the legs are noted by the variables, and . The variable represents the hypotenuse.

Substitute and solve for the hypotenuse.

Simplify.

Take the square root of both sides of the equation.

In each choice, the two shortest sides of the triangle are 9 and 12, so the third side can be found by applying the Pythagorean Theorem. Set in the Pythagorean equation and solve for :

Take the square root:

.

The correct choice is

.

Step 1: Recall the Pythagorean theorem statement and formula.

Statement: For any right triangle, the sums of the squares of the shorter sides is equal to the square of the longest side.

Formula: In a right triangle , If are the shorter sides and is the longest side.. then,

Step 2: Plug in the values given to us in the problem....

Evaluate:

Simplify:

Simplify:

Take the square root...

Step 3: Simplify the root...

The length of the hypotenuse in most simplified form is cm.