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.
To find the length of the hypotenuse of a right triangle when the lengths of the legs are known, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Given that both legs are 12 cm long, you can set up the equation as follows:
Hypotenuse^2 = Leg1^2 + Leg2^2
Hypotenuse^2 = 12^2 + 12^2
Hypotenuse^2 = 144 + 144
Hypotenuse^2 = 288
Next, take the square root of both sides to solve for the hypotenuse:
Hypotenuse = √288
Hypotenuse ≈ 16.97 cm
Rounded to the nearest hundredth, the length of the hypotenuse is 16.97 cm. Thus, the correct answer is:
16.97