Can someone check my answer?

Find the measure of EC:

For some reason I got 1 ft but I feel like it's the wrong answer.

CE measures 1 ft (so you’re correct)

Step-by-step explanation: What we have in the diagram are two similar triangles placed one inside the other. Upon careful observation we would see that one triangle is BCA and the other triangle is DEA.

Also we notice here that line BC is parallel to line DE. The next step is to find the ratios of similarity between both triangles.

We can determine that

Line BC/line CA = Line DE/line EA

Also we observe that

Line BD/line BA = line CE/line CA

Yet again, we observe that

Line BD/line DA = line CE/line EA.

With these ratios we can now determine the measure of CE

If BD/DA = CE/EA, then

2/8 = CE/4

By cross multiplication we now have

2 x 4 = 8 x CE

8 = 8CE

Divide both sides of the equation by 8

CE = 1

And just to be sure, we can use another ratio as follows;

If BD/BA = CE/CA

2/10 = CE/{4 + CE}

(Remember that line BA = 2 + 10)

By cross multiplication we now have

2 {4 + CE} = 10 x CE

8 + 2CE = 10CE

By collecting like terms we have

8 = 10CE - 2CE

8 = 8CE

Divide both sides of the equation by 8

CE = 1