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

In a right triangle, the relationship between the lengths of the legs and the hypotenuse is described by the Pythagorean theorem. This theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

For this particular triangle with legs measuring 3 and 4, you can apply the theorem as follows:

1. Square the lengths of the legs:

• (3^2 = 9)

• (4^2 = 16)

2. Add these squared lengths together:

• (9 + 16 = 25)

3. Take the square root of the sum to find the length of the hypotenuse:

• (\sqrt{25} = 5)

This calculation confirms that the value of the hypotenuse is indeed 5. Therefore, the correct answer reflects the application of the Pythagorean theorem accurately, leading to a correct determination of the triangle's hypotenuse length.