#### Question

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

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

Solution In the Following Figure, De || Bc Such that Ae = (1/4) Ac. If Ab = 6 Cm, Find Ad. Concept: Criteria for Similarity of Triangles.