How do u find the length of the hyotenudr of a right triangle

To find the length of the hypotenuse of a right triangle, you can use 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 \( b \). This can be expressed with the formula:

\[
c^2 = a^2 + b^2
\]

To find the length of the hypotenuse \( c \), follow these steps:

1. Measure the lengths of the two legs (the two sides that are not the hypotenuse), which are denoted as \( a \) and \( b \).
2. Square both lengths: \( a^2 \) and \( b^2 \).
3. Add those two squares together: \( a^2 + b^2 \).
4. Take the square root of the sum to find \( c \):

\[
c = \sqrt{a^2 + b^2}
\]

### Example:

If one leg measures 3 units and the other leg measures 4 units:
1. \( a = 3 \)
2. \( b = 4 \)
3. Calculate \( c \):

\[
c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

So, the length of the hypotenuse is 5 units.