Question

13. If AC = 16, DE = 8 and BE = 6, find AE. Please show all work

Answer 1

AE = 4

Explanation:

Use the formula

AE*EC = DE*EB

Since we don't know AE or EC, let AE = x and then EC will = 16 - x. The formula then becomes

x(16 - x) = 8(6)

`16x-x^2=48`

Getting everything on one side and setting it equal to 0 will allow us to factor for x:

`x^2-16x+48=0`

Factoring that gives you that

x = 4 and x = 12. That means that one of those sements has a length of 4 and the other has a length of 12. AE is shorter so it's 4 and EC = 12