Question

please help question is in the picture!!

Answer 1

Answer:

Length of AD is 8 unit

Step-by-step 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,

$\frac{BD}{BE}$ = $\frac{AB}{AC}$

⇒ $\frac{x}{x + 3}$ = $\frac{14}{21}$

⇒ $\frac{x}{x + 3}$ = $\frac{2}{3}$

⇒ 3x  = 2x + 6

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

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