Question

ABC is triangle D is a Point on AB Such that AD=1/4 AB
E is the on AC such that
such that AE = 1/4 AC.If DE=2cm
find BC
​

Answer 1

Let P and Q be the midpoints of AB and AC respectively. Read more on Sarthaks.com - https://www.sarthaks.com/112588/abc-is-triangle-is-point-on-ab-such-that-ad-ab-and-is-point-on-ac-such-that-ae-ac-prove-that-de-bc

Answer 2

Answer:

AD=41 and ACAE=41                                          [Given]

∴ABAD=ACAE

⇒DE∥BC                                                         [By converse of basic proportionality theorem]

In △ADE and △ABC,

∠ADE=∠B                                                       [Pair of corresponding angles]

∠AED=∠C                                                       [Pair of corresponding angles]

Hence, △ADE∼△ABC                                  [By AA similarity criteria]

Therefore,

ABAD=ACAE=BCDE                                                 [Corresponding sides of similar triangles are proportional]

∴BCDE=41

⇒BC=4DE

⇒BC=4×2

⇒BC=8cm