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    ΔEFG and ΔHIJ are similar. Also, ∠E = ∠H and ∠F = ∠I. If 3EF = HI and FG = 9 cm, then IJ is equal to ____.
    Question

    ΔEFG and ΔHIJ are similar. Also, ∠E = ∠H and ∠F = ∠I. If 3EF = HI and FG = 9 cm, then IJ is equal to ____.

    A.

    9 cm

    B.

    27 cm

    C.

    3 cm

    D.

    18 cm

    Correct option is B

    Given:

    ​∠E = ∠H and ∠F = ∠I

    3EF = HI

    FG = 9 cm

    Solution:

    As ΔEFG and ΔHIJ are similar,

    Let's take an example, when EF = 1 unit, then HI = 3 units.

    As per the similarity theorem,

    EFHI=FGIJ=EGHJ\frac{EF}{HI}=\frac{FG}{IJ}=\frac{EG}{HJ}​​

    Putting the values, we get

    13=9IJ\frac{1}{3}=\frac{9}{IJ}​​

    IJ = 9 ×\times​ 3 = 27

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