In △ABC, D and E are the points on sides AB and AC, respectively, such that DE ll BC. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, then (AB + EC) is equal to (all measurements in cm):
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 9.
Since DE || BC, AD/DB = AE/EC
x/(x - 2) = (x + 2)/(x - 1)
⇒ x2 - x = x2 - 4
⇒ -x = -4
⇒ x = 4
AB = AD + DB = x + (x - 2) = 4 + 2 = 6 cm
EC = x - 1 = 3 cm
AB + EC = 6 + 3 = 9 cm