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 Not enough information is given to solve the problem. Not enough information is given to solve the problem. 288 288 17.0 17.0 16.97 choose
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
In this case, since both legs of the triangle are 12 cm long, you can use the Pythagorean theorem to find the length of the hypotenuse.
Let's denote the length of the hypotenuse as c and the length of each leg as a. Using the Pythagorean theorem, we have:
c^2 = a^2 + a^2
c^2 = 2a^2
c = √(2a^2)
Substituting a = 12, we get:
c = √(2 * 12^2)
c ≈ 16.97 cm
So, the length of the hypotenuse is approximately 16.97 cm, rounded to the nearest hundredth.
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of one leg as a and the length of the other leg as b, and the length of the hypotenuse as c.
In this case, we are given that both legs are 12 cm long, so a = b = 12 cm.
Using the Pythagorean theorem, we can write:
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To solve for c, we need to take the square root of both sides:
c = √288
Using a calculator, we find that √288 ≈ 16.97.
Rounding to the nearest hundredth, the length of the hypotenuse is 16.97 cm.
Therefore, the answer is 16.97.
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 (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
In this case, since both legs of the right triangle are 12 cm long, we can label them a and b. The length of the hypotenuse will be represented by c.
The Pythagorean Theorem equation is: a^2 + b^2 = c^2
Plugging in the values, we have: 12^2 + 12^2 = c^2
Simplifying this equation, we get: 144 + 144 = c^2
Adding 144 and 144, we get: 288 = c^2
To find the length of the hypotenuse, we need to find the square root of both sides of the equation, since the hypotenuse is the square root of the sum of the squares of the legs.
Taking the square root of 288, we get approximately 16.97 (rounded to the nearest hundredth). Therefore, the length of the hypotenuse is approximately 16.97 cm.
Hence, the correct answer is: 16.97