Given D,E, and F are collinear points, E is between D and F, DE is six times the length of EF, and DF=84 units, find the length of seg

Question

Given D,E, and F are collinear points, E is between D and F,
DE is six times the length of EF, and DF=84 units, find the length of segment DE.

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Thiên Ân 1 year 2021-09-03T16:09:47+00:00 1 Answers 5 views 0

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    2021-09-03T16:11:39+00:00

    Answer:

    72 units

    Step-by-step explanation:

    Given D,E, and F are collinear points and E is between D and F, then the expression DE + EF = DF…. 1 is true

    If DE is six times the length of EF, then;

    DE = 6DF

    DF = DE/6 …..2

    Substitute equation 2 into 1;

    DE + EF = DF

    DE + DE/6 = DF

    find the LCM

    (6DE+DE)/6 = DF

    cross multiply

    6DE+DE = 6DF

    7DE = 6DF

    Given DF = 84units

    7DE = 6(84)

    7DE = 504

    Divide both sides by 7

    7DE/7 = 504/7

    DE = 72

    Hence  the length of segment DE is 72units

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