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)

Question

Responses

Not enough information is given to solve the problem.
Not enough information is given to solve the problem.

17.0
17.0

16.97
16.97

288
288

Answer 1

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

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, both legs \( a \) and \( b \) are 12 cm.

So, substituting the values into the formula:

\[ c = \sqrt{12^2 + 12^2} = \sqrt{144 + 144} = \sqrt{288} \]

Now, calculate \( \sqrt{288} \):

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

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

Therefore, the correct response is:

16.97