Answer:
Step-by-step 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
