If AC = 20, AE = 25, and AB = 5, what is the length of AD?

What is D? What figure are you talking about?

To find the length of AD, we can use the Pythagorean theorem.

Given: AC = 20, AE = 25, and AB = 5.

Step 1: Find the length of CD:
Using the Pythagorean theorem, we have:
AC^2 = AD^2 + CD^2
20^2 = AD^2 + CD^2
400 = AD^2 + CD^2

Step 2: Find the length of CE:
Using the Pythagorean theorem, we have:
AC^2 = AE^2 + CE^2
20^2 = 25^2 + CE^2
400 = 625 + CE^2

Step 3: Find the length of DE:
Using the Pythagorean theorem, we have:
CE^2 = AD^2 + DE^2
625 + CE^2 = AD^2 + DE^2

Step 4: Substitute the values from Step 1, Step 2, and Step 3 into equations:
400 = AD^2 + CD^2
400 = 625 + CE^2
625 + CE^2 = AD^2 + DE^2

Step 5: Solve the system of equations:
From Step 2, we can find CE^2 = 400 - 625 = -225, which is not possible since the length of a side cannot be negative. Therefore, there is no solution for the length of AD.

To find the length of AD, we can use the properties of triangles and apply the Pythagorean theorem.

First, let's draw a diagram of the triangle ABC:

```
A
/\
25/ \5
/ \
/______\
B 20 C
```

Now, let's label the points on the diagram:

- Point A is the top vertex of the triangle.
- Point B is the bottom-left vertex of the triangle.
- Point C is the bottom-right vertex of the triangle.
- Point D is the point on BC that is perpendicular to AB.
- Point E is the point on AC that is perpendicular to AB.

We have been given the following information:
- AC = 20
- AE = 25
- AB = 5

Using the Pythagorean theorem, we know that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In triangle ADE, AD is the hypotenuse, and AE and DE are the other two sides. So, we can use the Pythagorean theorem to find AD:

AD^2 = AE^2 + DE^2

Now, let's find DE. Triangle ABC is a right-angled triangle, so we can use the Pythagorean theorem to find the length of DE:

DE^2 = AC^2 - AE^2

Substituting in the values we know:

DE^2 = 20^2 - 25^2
DE^2 = 400 - 625
DE^2 = -225

Uh-oh! We've encountered a problem. The square of a length cannot be negative. This means that the given values of AC, AE, and AB cannot form a valid triangle.

Please double-check your values or provide additional information if needed.