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    In ∆ABC, D and E are points on sides AB and AC, respectively, such that DE || BC and AD : DB = 3: 1. If EA = 3.3 cm, then find the value of AC.
    Question

    In ∆ABC, D and E are points on sides AB and AC, respectively, such that DE || BC and AD : DB = 3: 1. If EA = 3.3 cm, then find the value of AC.

    A.

    4 cm

    B.

    1.1 cm

    C.

    5.5 cm

    D.

    4.4 cm

    Correct option is D

    Given:
    In ΔABC , D and E are points on sides AB and AC respectively such that DE∥BC.
    The ratio AD : DB = 3 : 1.
    EA = 3.3cm.
    Concept Used:
    Since DE∥BC, by the Basic Proportionality Theorem (Thales' Theorem), the ratio of the segments on the sides of the triangle will be the same:
    ADDB=AEEC\frac{AD}{DB} = \frac{AE}{EC}​​
    Solution:
    By Thales theorem:
    AEEC=ADDB 3.3EC=31  EC=1.1 cm\frac{AE}{EC}=\frac{AD}{DB}\\ \ \\\frac{3.3}{\text{EC}} = \frac{3}{1} \\ \ \\\implies \text{EC} = 1.1 \, cm​​
    Now, AC = AE + EC = 3.3 + 1.1 = 4.4 cm
    Thus, The length of AC is 4.4 cm.

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