Question

If a right triangle has side lengths that are 12 in. and 16 in. long, how long is the hypotenuse?

Answer 1

To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is:

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

In this case, let \( a = 12 \) inches and \( b = 16 \) inches.

Now, we can calculate \( c \):

\[
c^2 = 12^2 + 16^2
\]
\[
c^2 = 144 + 256
\]
\[
c^2 = 400
\]

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

\[
c = \sqrt{400}
\]
\[
c = 20 \text{ inches}
\]

Thus, the length of the hypotenuse is **20 inches**.