Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Isosceles triangle $ABE$ of area 100 square inches is cut by $\overline{CD}$ into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 75 square inches. If the altitude of triangle $ABE$ from $A$ is 20 inches, what is the number of inches in the length of $\overline{CD}$?

[asy]
draw((-9,0)--(0,24)--(9,0)--cycle);
draw((-6,8)--(6,8));
label("$A$",(0,24),N);
label("$B$",(-9,0),W);
label("$C$",(-6,8),NW);
label("$D$",(6,8),NE);
label("$E$",(9,0),E);
[/asy]
user