Question

In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC. 

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

Answer 1

We have,

DE || BC

Now, In ΔADE and ΔABC

∠A = ∠A [common]

∠ADE = ∠ABC [∵ DE || BC ⇒ Corresponding angles are equal]

⇒ ΔADE ~ ΔABC [By AA criteria]

`rArr"AB"/"BC"="AD"/"DE"`

`rArr"AB"=(2.4xx5)/2`

⇒ AB = 1.2 × 5 = 6.0 cm

⇒ AB = 6 cm

∴ BD = 6 cm

BD = AB – AD

= 6 – 2.4 = 3.6 cm

⇒ DB = 3.6 cm

Now,

`"AC"/"BC"="AE"/"DE"`         [∵ Corresponding sides of similar triangles are equal]

`rArr"AC"/5=3.2/2`

`rArr"AC"=(3.2xx5)/2=1.6xx5=8.0 ` cm

⇒ AC = 8 cm

∴ CE = AC – AE

= 8 – 3.2 = 4.8 cm

Hence, BD = 3.6 cm and CE = 4.8 cm