Question

In ∆ABC, DE\\BC. If AD = 2.4cm, AE =3.2cm, DE = 2cm and BC = 5cm, find BD and CE.

Answer 1

In triangles ABC and ADE,
AD/DB = DE/BC
2.4/DB = 2/5
5 × 2.4 = 2 × DB
12 = 2 × DB
6 cm = DB.

In triangle ABC,
AD/DB = AE/EC
2.4/6 = 3.2/EC
2.4 × EC = 3.2 × 6
2.4 × EC = 19.2
EC = 19.2/2.4 * 10
EC = 192/24
EC = 8 cm.

Therefore, BD = 6cm and CE = 8cm.

Answer 2

Step-by-step explanation:

AD/AB=DE/BC

2.4/2.4+DB=2/5

2.4×5=(2.4+DB)×2

12=4.8+2DB

12-4.8/2=DB

3.6cm=DB

AE/AC=DE/BC

3.2/3.2+EC=2/5

3.2×5=(3.2+EC)2

16=6.4+2EC

16-6.4/2=EC

4.8cm=EC