To find the length of side \(AC\), we can use the Pythagorean theorem since \(AC\) is the hypotenuse of a right triangle \(ABC\).
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (\(AC\)) is equal to the sum of the squares of the lengths of the other two sides (\(AB\) and \(BC\)).
So, \(AC^2 = AB^2 + BC^2\).
Given that \(AB = 9\) cm and \(BC = 9\) cm, we can substitute these values into the equation:
AC^2 = 9^2 + 9^2
AC^2 = 81 + 81
AC^2 = 162
Now, we can find AC by taking the square root of both sides:
AC = root under 162
AC = 12.727 cm.
Therefore, the length of side AC is approximately 12.727 cm.
