If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

Step 1: Identify the lengths of the legs of the right triangle. Here, one leg is 3 cm and the other leg is 4 cm.
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 = 3 cm and b = 4 cm, so we have: c² = 3² + 4².
Step 4: Calculate the squares of the legs. 3² = 9 and 4² = 16.
Step 5: Add the squares together. 9 + 16 = 25.
Step 6: To find the length of the hypotenuse, take the square root of the sum. So, c = √25.
Step 7: Calculate the square root. √25 = 5 cm.
Step 8: Therefore, the length of the hypotenuse is 5 cm.

Pythagorean Theorem – The 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 other two sides.