Question

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

Answer 1

Answer:

AE = 4

Step-by-step 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