Question

Given that AE∥BD, identify the length of AC. HELP ASAP!!

Answer 1

Answer: Choice D) 22.5

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Explanation:

x = length of BC

AC = AB+BC

AC = 6 + x

CE = CD+DE

CE = 22+8

CE = 30

Triangles ACE and BCD are similar triangles (can be proven by the AA similarity theorem due to the fact that AE || BD)

Therefore the corresponding sides are proportional letting us set up the proportion below

AC/BC = CE/CD

(6+x)/x = 30/22 .... substitution

22(6+x) = 30x ... cross multiply

132+22x = 30x

132 = 30x-22x ..... subtract 22x from both sides

132 = 8x

8x = 132

x = 132/8 .... divide both sides by 8

x = 16.5

Now use this to find the length of AC

AC = 6+x

AC = 6+16.5

AC = 22.5