Question

In the following figure, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD.

Answer 1

We have, DE || BC, AB = 6 cm and AE `= 1/4` AC

In ΔADE and ΔABC

∠A = ∠A                          [Common]

∠ADE = ∠ABC                  [Corresponding angles]

Then, ΔADE ~ ΔABC         [By AA similarity]

`rArr"AD"/"AB"="AE"/"AC"`             [Corresponding parts of similar Δ are proportional]

`rArr"AD"/6=(1/4AC)/"AC"`                [∵ AE `=1/4` AC given]

`"AD"/6=1/4`

`rArr"AD"=6/4=1.5` cm