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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.

User Gprime
by
8.0k points

1 Answer

4 votes

Answer:

72 units

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

User Eric Long
by
8.0k points
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