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  1. d. bc = 12 and ef = 16

    step-by-step explanation:

    we are given that δabc : δdef such that [tex]\frac{ab}{de}=\frac{bc}{ef}[/tex].

    also, it is given that [tex]\frac{ab}{de}=\frac{3}{4}[/tex]

    so, from the options, we need that [tex]\frac{bc}{ef}=\frac{3}{4}[/tex].

    a. [tex]\frac{bc}{ef}=\frac{6}{9}=\frac{2}{3}[/tex]

    b. [tex]\frac{bc}{ef}=\frac{4}{6}=\frac{2}{3}[/tex]

    c.   [tex]\frac{bc}{ef}=\frac{8}{12}=\frac{2}{3}[/tex]

    d. [tex]\frac{bc}{ef}=\frac{12}{16}=\frac{3}{4}[/tex]

    as, we can see that only option d gives the same ratio as [tex]\frac{ab}{de}=\frac{3}{4}[/tex] i.e. [tex]\frac{bc}{ef}=\frac{3}{4}[/tex].

    hence, the possible lengths are bc = 12 and ef = 16.

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