Question

Use the Pythagorean theorem to find the unknown side of the right triangle.
9
12



A right triangle has a vertical side of length 9, a horizontal side of length 12, and an unlabeled hypotenuse.
Question content area bottom
Part 1
Hypotenuse lengthequals
  
StartRoot 225 EndRoot
​(Simplify your answer. Type exact​ answers, using radicals as​ needed.)

Answer 1

To find the length of the hypotenuse of a right triangle using the Pythagorean theorem, you use the formula:

\[
c^2 = a^2 + b^2
\]

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case:

- \(a = 9\)
- \(b = 12\)

Now, plug in the values:

\[
c^2 = 9^2 + 12^2
\]

Calculating the squares:

\[
c^2 = 81 + 144
\]

Adding those together:

\[
c^2 = 225
\]

Now, take the square root to find \(c\):

\[
c = \sqrt{225}
\]
\[
c = 15
\]

Thus, the length of the hypotenuse is \(15\). However, it seems you've provided a different context by stating "StartRoot 225 EndRoot."

To give you an exact answer in the requested format:

\[
\text{Hypotenuse length} = 15
\]

and in radical form:

\[
= \sqrt{225}
\]

So the simplified exact answer is either \(15\) or \( \sqrt{225} \).