To find the length of the hypotenuse of a right triangle with legs measuring 15 and 20, you can use the Pythagorean theorem, which states:
\[ c = \sqrt{a^2 + b^2} \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case:
\[ a = 15, \quad b = 20 \]
Now substitute these values into the formula:
\[ c = \sqrt{15^2 + 20^2} \]
Calculating the squares:
\[ 15^2 = 225, \quad 20^2 = 400 \]
Now add them together:
\[ c = \sqrt{225 + 400} = \sqrt{625} \]
Finally, take the square root:
\[ c = 25 \]
Therefore, the length of the hypotenuse is 25.