Answer: x = 4
Explanation:
First, let's find the length of side AD. We will need this information for later. We can find this with the pythagorean theorem. We know that AB = 20 and BD = 40 since sides BE and ED add up to 40.
a^2 + b^2 = c^2
20^2 + b^2 = 40^2
b ≈ 34.64 (side AD)
Now, let's find side CE. Since CE and AD are parallel to each other, triangles BCE and BAD are similar triangles. Let's set up a proportion to solve for CE.
CE/AD = BE/BD. These sides are the same corresponding sides in each of the triangles.
CE/34.64 = 16/40
Now solve for CE.
CE = 13.856
Now let's solve for side BC using the pythagorean theorem again.
a^2 + b^2 = c^2
a^2 + 13.856^2 = 16^2
a ≈ 8 (side BC)
Now we have all the information we need to solve for x.
AC + BC = AB
3x + 8 = 20
3x = 12
x = 4
I know it can be hard to visualize everything at once, so I provided a picture of the triangle but labeled with its lengths.