Respuesta :

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|DF| = |DE| + |EF|

|DF| = 9x -36

|DE| = 47

|EF| = 3x+10

Substitute:

9x - 39 = 47 + 3x + 10

9x - 39 = 3x + 57     |+39

9x = 3x + 96    |-3x

6x = 96    |:6

x = 16

Put the value of x to the equation |EF| = 3x + 10

|EF| = (3)(16) + 10 = 48 + 10 = 58

Answer: |EF| = 58

Answer:  The required length of EF is 58 units.

Step-by-step explanation:  Given that DF = 9x - 39, DE = 47 units and EF = 3x + 10.

We are to find the length of EF.

We have

[tex]DE+EF=DF\\\\\Rightarrow 47+(3x+10)=9x-39\\\\\Rightarrow 3x+57=9x-39\\\\\Rightarrow 9x-3x=57+39\\\\\Rightarrow 6x=96\\\\\Rightarrow x=\dfrac{96}{6}\\\\\Rightarrow x=16.[/tex]

Therefore, the length of EF is given by

[tex]EF=3\imes16+10=48+10=58.[/tex]

Thus, the required length of EF is 58 units.

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