contestada

In the diagram below of triangle
B
C
D
BCD,
E
E is a midpoint of
B
C
‾
BC
and
F
F is a midpoint of
C
D
‾
CD
. If
E
F
=
6
x
−
31
EF=6x−31, and
B
D
=
64
−
9
x
BD=64−9x, what is the measure of
E
F
EF?

Respuesta :

sqdancefan

9514 1404 393

Answer:

  EF = 5

Step-by-step explanation:

Given:

  EF = 6x -31

  BD = 64 -9x

  BD = 2·EF

Find:

  EF

Solution:

  BD = 2·EF

  64 -9x = 2(6x -31) . . . . substitute the given expressions

  64 -9x = 12x -62  . . . .  eliminate parentheses

  126 = 21x . . . . . . . . . . . add 62+9x

  x = 6 . . . . . . . . . . . . . . . divide by 21

Now the length of EF is ...

  EF = 6x -31 = 6(6) -31

  EF = 5

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