What is the hypotenuse of a right triangle with legs measuring 3 cm and 4 cm?

To find the hypotenuse of a right triangle with leg lengths of 3 cm and 4 cm, you can apply the 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).

In this case, the legs of the triangle are:

• a = 3 cm

• b = 4 cm

Using the Pythagorean theorem:

c² = a² + b²

c² = (3 cm)² + (4 cm)²

c² = 9 cm² + 16 cm²

c² = 25 cm²

To find the length of the hypotenuse (c), take the square root of both sides:

c = √(25 cm²)

c = 5 cm

Therefore, the length of the hypotenuse is 5 cm, which confirms that the correct answer is indeed 5 cm. This reasoning directly aligns with the properties of right triangles described by the Pythagorean theorem, enabling you to accurately determine the relationship between the sides.