Question

Need help figuring this out and would like you to explain how you did it please.

Answer 1

Explanation:

GIVEN THAT

DE ||AC

SO BY BASIC PROPORTIONALITY THEOREM

BD. BE

----- = ------

DA. EC

SO a = 24. (Substituting values)

Thanks

Answer 2

Explanation:

Since DE is parallel to AC, then triangle DBE is similar to triangle ABC. It means that

AB/DB = BC/BE = AC/DE

Also, the length of BA is BD + DA

BD + DA = 18 + 36 = 54

Also, BC = BE + EC

BC = a + 12

Since triangle DBE is similar to triangle ABC, then

DB/AB = EB/CB. Therefore,

18/54 = a/(a + 12)

Cross multiplying the left hand side of the equation by (a + 12) and the right hand side of the equation by a, it becomes

18(a + 12) = 54 × a

18a + 216 = 54a

Subtracting 18a from the left hand side of the equation and the right hand side of the equation by , it becomes

18a - 18a + 216 = 54a - 18a

36a = 216

Dividing the left hand side of the equation and the right hand side of the equation by 36, it becomes

36a/36 = 216/36

a = 6