If the lengths of the legs of a right triangle are 12 and 16, what is the length

₹0.0

Question: If the lengths of the legs of a right triangle are 12 and 16, what is the length of the hypotenuse?

Options:

Correct Answer: 20

Solution:

Using the Pythagorean theorem, c = √(12² + 16²) = √(144 + 256) = √400 = 20.

If the lengths of the legs of a right triangle are 12 and 16, what is the length of the hypotenuse?

If the lengths of the legs of a right triangle are 12 and 16, what is the length of the hypotenuse?

Step 1: Identify the lengths of the legs of the right triangle. They are 12 and 16.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as c² = a² + b².
Step 3: Substitute the lengths of the legs into the formula. Here, a = 12 and b = 16, so we have c² = 12² + 16².
Step 4: Calculate 12², which is 144.
Step 5: Calculate 16², which is 256.
Step 6: Add the results from Step 4 and Step 5 together: 144 + 256 = 400.
Step 7: To find the length of the hypotenuse (c), take the square root of 400. This means c = √400.
Step 8: Calculate the square root of 400, which is 20.
Step 9: Therefore, the length of the hypotenuse is 20.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).