In △ABC, D and E are points on the sides AB and AC, respectively, such that DE||BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 12.7
Let DE = x and EC = y.
DE || BC so we can say that △ABC is similar to △ADE by AA.
AD/AB = DE/BC = AE/AC
5/14 = x/15.4 = 4/4+y
On solving further we gey,
x = 5.5 and y = 7.2
x + y = 5.5 + 7.2 = 12.7.