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
