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

1 answer

To find the length of the hypotenuse of a right triangle with both legs measuring 12 cm, you can use the Pythagorean theorem, which states:

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

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

In this case, both legs are equal:

\[ a = 12 , \text{cm} \quad \text{and} \quad b = 12 , \text{cm} \]

So, substituting in the values:

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

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

\[ c = \sqrt{288} \approx 16.97 \]

Thus, the length of the hypotenuse, rounded to the nearest hundredth, is:

\[ \boxed{16.97} \]