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In the Following Figure, De || Bc Such that Ae = (1/4) Ac. If Ab = 6 Cm, Find Ad. - CBSE Class 10 - Mathematics

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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

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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.
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