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
16.97
16.97
288
288
Not enough information is given to solve the problem.
Not enough information is given to solve the problem.
To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the lengths of both legs are given as 12 cm. Therefore, we can calculate the length of the hypotenuse as follows:
Hypotenuse^2 = Leg1^2 + Leg2^2
Hypotenuse^2 = 12^2 + 12^2
Hypotenuse^2 = 144 + 144
Hypotenuse^2 = 288
Taking the square root of both sides, we get:
Hypotenuse = √288
Rounding to the nearest hundredth, we find that the length of the hypotenuse is approximately 16.97 cm.
Therefore, the correct answer is:
16.97
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, since both legs of the right triangle are 12 cm long, you can substitute these values into the theorem:
hypotenuse^2 = leg1^2 + leg2^2
hypotenuse^2 = 12^2 + 12^2
hypotenuse^2 = 144 + 144
hypotenuse^2 = 288
To find the length of the hypotenuse, you need to take the square root of both sides:
hypotenuse = √288
Now, you can use a calculator to find the square root of 288 and round the answer to the nearest hundredth.
The correct answer is 16.97 cm.