What is the length of the hypotenuse of a right triangle with legs of lengths 5

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Question: What is the length of the hypotenuse of a right triangle with legs of lengths 5 cm and 12 cm?

Options:

Correct Answer: 13 cm

Solution:

Using the Pythagorean theorem, hypotenuse = √(5^2 + 12^2) = √(25 + 144) = √169 = 13 cm.

What is the length of the hypotenuse of a right triangle with legs of lengths 5 cm and 12 cm?

What is the length of the hypotenuse of a right triangle with legs of lengths 5 cm and 12 cm?

Step 1: Identify the lengths of the legs of the right triangle. Here, one leg is 5 cm and the other leg is 12 cm.
Step 2: Use the Pythagorean theorem formula, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is c^2 = a^2 + b^2.
Step 3: Substitute the lengths of the legs into the formula. So, we have c^2 = 5^2 + 12^2.
Step 4: Calculate the squares of the legs. 5^2 = 25 and 12^2 = 144.
Step 5: Add the squares together. 25 + 144 = 169.
Step 6: To find the length of the hypotenuse, take the square root of 169. So, c = √169.
Step 7: Calculate the square root. √169 = 13.
Step 8: Therefore, the length of the hypotenuse is 13 cm.

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