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In a ΔABC, D and E are points on AB and AC respectively, such that DE ∥ BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm. Find BD and CE.

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Question taken from RD sharma
Class 10th
Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions.

In this question we have In a ΔABC, D and E are points on AB and AC respectively,

Also it is given that DE ∥ BC.

AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm.

Now we have to Find BD and CE.

 

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RD sharma, DHANPAT RAI publication

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1 Answer

  1. Given:

    In Δ ABC,

    Length of side AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BE = 5 cm

    Also, DE ∥ BC

    To find: Length of side BD and CE.

    As DE ∥ BC, AB is transversal,

    ∠APQ = ∠ABC (corresponding angles)                        – equation 1

    As DE ∥ BC, AC is transversal,

    ∠AED = ∠ACB (corresponding angles)                         – equation 2

    In Δ ADE and Δ ABC,

    Now from equation 1 and 2 we get,

    ∠ADE = ∠ABC

    ∠AED = ∠ACB

    ∴ ΔADE = ΔABC (By AA similarity criteria)

    Now, we know that

    Corresponding parts of similar triangles are proportional.

    Therefore,

    ⇒ AD/AB = AE/AC = DE/BC

    AD/AB = DE/BC

    2.4/ (2.4 + DB) = 2/5 [Since, length of side AB = AD + DB]

    2.4 + DB = 6

    DB = 6 – 2.4

    DB = 3.6 cm

    Length of side DB is 3.6 cm

    In the same way, we get

    ⇒ AE/AC = DE/BC

    3.2/ (3.2 + EC) = 2/5 [Since AC = AE + EC]

    3.2 + EC = 8

    EC = 8 – 3.2

    EC = 4.8 cm

    ∴ BD = 3.6 cm and CE = 4.8 cm.

    Length of side BD is 3.6 cm and CE is 4.8 cm

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