Question

If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.(1 point)
Responses

288
288
16.97
16.97
17.0
17.0
Not enough information is given to solve the problem.

Answer 1

To find the length of the hypotenuse of a right triangle when both legs are the same length (12 cm), we can use the Pythagorean theorem, which states:

\[
c = \sqrt{a^2 + b^2}
\]

Where:
- \(c\) is the length of the hypotenuse,
- \(a\) and \(b\) are the lengths of the legs.

In this case, both legs are 12 cm:

\[
c = \sqrt{12^2 + 12^2}
\]
\[
c = \sqrt{144 + 144}
\]
\[
c = \sqrt{288}
\]
\[
c \approx 16.97 \text{ cm}
\]

Rounding to the nearest hundredth, the length of the hypotenuse is approximately 16.97 cm.

Therefore, the correct answer is **16.97**.