To find the length of AC given CE = 101 and AE = 99, we can use the Pythagorean theorem if we are dealing with a right triangle (assuming C and E are points on the triangle as corners).
If the triangle is right-angled at A, then you can set up the equation as follows:
Using the notation:
- AC = x (the length we want to find)
- AE = 99 (one side)
- CE = 101 (the other side)
The equation according to the Pythagorean theorem would be:
\[ AC^2 + AE^2 = CE^2 \] \[ x^2 + 99^2 = 101^2 \]
Expanding this gives: \[ x^2 + 9801 = 10201 \]
To solve for x^2: \[ x^2 = 10201 - 9801 \] \[ x^2 = 400 \]
Now taking the square root: \[ x = \sqrt{400} \] \[ x = 20 \]
Thus, AC = 20.
To summarize, if you are looking for AC based on the given lengths: AC = 20.