Question

Please help question is in the picture!!

Answer 1

Length of AD is 8 unit

Explanation:

Let, BD = x unit ,

then, according to the question, BE = (3 + x) unit

AB = 14 unit and BC = 21 unit (given)

Now, in Δ ABC, D and E are over AB and BC respectively and DE ║BC

So, Δ ABC and Δ BDE are similar or Δ ABC
`\sim` Δ BDE

So, we get,

`(BD)/(BE)` =
`(AB)/(AC)`

⇒
`(x)/(x + 3)` =
`(14)/(21)`

⇒
`(x)/(x + 3)` =
`(2)/(3)`

⇒ 3x = 2x + 6

⇒ x = 6 ----------------------------------(1)

So, AD = AB - BD = (14 - x) unit = 8 unit [from (1)]