In △ABC, ∠B = 87° and ∠C = 60°. Points D and E are on the side AB and AC, respectively, such that ∠DEC = 93° and DE : BC = 5 : 9. If AB = 14.4 cm, then the length of AE is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8 cm.
In ΔABC, ∠A = 180° - 87° - 60° = 33°
∠EDB = 360° - 93° - 60° - 87° = 120°
∠ADE = 180° - 120° = 60°
∠AED = 180° - 93° = 87°
ΔADE ~ ΔACB
DE/BC = AE/AB
⇒ AE = (DE/BC) × AB
⇒ AE = 5/9 × 14.4 = 8 cm