Question

In ΔABC, D and E are the points on the sides AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm and CE = 4.8 cm, which of the following is the length BD?

Answer 1

Answer:

BD = 1.2 cm

Step-by-step explanation:

In ΔADE and ΔABC

∠ADE =∠ABC  (corresponding angles of triangle)

∠AED =∠ACB  (corresponding angles)

By AA

ΔADE  ~ ΔABC  

Therefore,

AD/AB = AE/AC = DE/BC

In similar triangles, the corresponding sides are proportional to each other.

So,

→ AD/AB = AE/EC

→ 2.4/AB = 3.2/4.8

→ AB = 4.8/3.2 × 2.4

→ AB = 3.6

Now,

AB = AD + BD

3.6 = 2.4 + BD

BD = 1.2

Hence, the length of BD is 1.2 cm.