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
Not enough information is given to solve the problem.
Not enough information is given to solve the problem.
17.0
17.0
16.97
The correct answer is 16.97 cm.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem. The Pythagorean 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 two legs.
In this case, the lengths of the legs are both 12 cm. Let's plug these values into the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To find the square root of 288, we can use a calculator or approximation method. The approximate value of the square root of 288 is 16.97. Rounding to the nearest hundredth, the length of the hypotenuse is approximately 16.97 cm.
To solve this problem, we can use the Pythagorean theorem, which 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 two legs.
In this case, both legs of the right triangle are given to be 12 cm long. Let's represent the lengths of the legs as a and b, where a = b = 12 cm. Let c represent the length of the hypotenuse.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Substituting the values of a and b, we get:
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To find the length of the hypotenuse, we need to take the square root of both sides of the equation:
c = √(288)
Using a calculator, we can find the square root of 288 to be approximately 16.97.
Therefore, the length of the hypotenuse is approximately 16.97 cm when rounded to the nearest hundredth.