In triangle ABC, D and E are points on sides AB and AC such that DE||BC. If AD=4 cm, DB=12 cm, AE=3 cm, and EC=9 cm, what is the ratio of the area of triangle ADE to the area of triangle ABC?
Show answer & explanation
Correct answer: B
Explanation
Given:
AD = 4 cm
DB = 12 cm
AE = 3 cm
EC = 9 cm
DE ∥ BC
By the formula:
If DE ∥ BC, then
ΔADE ∼ ΔABC
Ratio of areas = (Ratio of equal sides)²
AB = AD + DB
= 4 + 12
= 16
AC = AE + EC
= 3 + 9
= 12
AD / AB = 4 / 16 = 1/4
AE / AC = 3 / 12 = 1/4
Ratio of areas = (1/4)² = 1/16
ΔADE : ΔABC = 1 : 16