Question

D and E are respectively the points on the sides AB and AC of ΔABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then DE = ______.

Answer 1

D and E are respectively the points on the sides AB and AC of ΔABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then DE = 3 cm.

Explanation:

Since DE || BC, triangles ADE and ABC are similar,

So `(AD)/(AB) = (DE)/(BC)`. 

Here AB = AD + BD

= 2 + 3

= 5 

Hence `DE = (AD)/(AB) xx BC` 

= `2/5 xx 7.5` 

= 3 cm