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

Answer 1

To find the length of the hypotenuse in a right triangle with legs of equal lengths, you can use the Pythagorean theorem, which states:

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

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs of the triangle.

In this case, both legs are 12 cm:

\[
c^2 = 12^2 + 12^2
\]
\[
c^2 = 144 + 144
\]
\[
c^2 = 288
\]

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

\[
c = \sqrt{288}
\]
\[
c \approx 16.97 \, \text{cm}
\]

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

Thus, the correct response is **16.97**.