To find the length of the side of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the length of the unknown side as x. According to the given information, one side has a length of 7 centimeters, and the hypotenuse measures 25 centimeters.

Applying the Pythagorean theorem:

x^2 + 7^2 = 25^2

Simplifying the equation:

x^2 + 49 = 625

x^2 = 625 - 49

x^2 = 576

Taking the square root of both sides:

x = 576

x = 24

Therefore, the length of the side of the right triangle is 24 centimeters.