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. 170
2. 288
3. Not enough information is given to solve the problem
4. 16.97
The length of the hypotenuse in a right triangle can be found using the Pythagorean theorem, which states that 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 12 cm. Therefore, using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse^2 = 12^2 + 12^2 = 144 + 144 = 288
Taking the square root of both sides, we find:
hypotenuse = √288 ≈ 16.97
Therefore, the length of the hypotenuse is approximately 16.97 cm.
The correct answer is 4. 16.97.
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 hypotenuse is equal to the sum of the squares of the two legs.
In this case, the legs of the right triangle are both given to be 12 cm long. Let's call the length of the hypotenuse "c". Using the Pythagorean theorem, we can set up the equation:
c^2 = 12^2 + 12^2
Simplifying, we have:
c^2 = 144 + 144
c^2 = 288
To find the length of the hypotenuse, we take the square root of both sides of the equation:
c = √288
Calculating the square root using a calculator, we find:
c ≈ 16.97
Therefore, rounding the answer to the nearest hundredth, the length of the hypotenuse is approximately 16.97 cm. So the correct answer is option 4.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the two legs of the right triangle as a and b, and the length of the hypotenuse as c.
In this case, both legs are 12 cm long, so we have:
a = b = 12 cm
Using the Pythagorean theorem, we can write:
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To find the value of c, we need to take the square root of both sides:
c = sqrt(288) ≈ 16.97
Therefore, the length of the hypotenuse is approximately 16.97 cm.
So, the correct answer is 4. 16.97.