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Work out the length of BD in the diagram below

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Work out the length of BD in the diagram.




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  1. To determine the length of BDBD in the diagram, we can use the fact that triangles CDE\triangle CDE and CBA\triangle CBA are similar. In similar triangles, corresponding sides are proportional.

    The lengths given in the diagram are:

    • CD=3 cmCD = 3 \, \text{cm}
    • CE=6 cmCE = 6 \, \text{cm}
    • EA=15 cmEA = 15 \, \text{cm}

    Since CECE and CACA are corresponding sides, and CDCD and CBCB are also corresponding sides, we can set up the proportion:

    CDCB=CECA\frac{CD}{CB} = \frac{CE}{CA}CBCD=CACE

    Since CA=CE+EA=6+15=21 cmCA = CE + EA = 6 + 15 = 21 \, \text{cm}, we can substitute the values:

    3BD=621\frac{3}{BD} = \frac{6}{21}

    Solving this proportion will give us the length of BDBD.

    Let’s calculate:

    BD=3×216=636=10.5 cm

    So, the length of BDBD is 10.5 cm.