Given: BC=3x+47 DE=10 BD=27+x CE=x+26

Question

What is the length of segment CE?

Answer 1

Because  Lines BD and CE are parallel,   BCDE is a trapezoid. 

Solving for the intersection of DE and CE  is easy because DE is parallel to the x axis.  The result is E: (-16,10)

Similarly for DE and BD        D:  (-16,10)

The intersection of CB and BD is harder but gives     B:  (-10 , 17)

  Similarly the intersection of CB and CE gives     C: (-21/2 , 31/2 )

 

Since C and E are now known, the distance formula can be used to get the length of CE

  The result is 11 x sqrt(2) /2

 

Answer 2

Two equations with two variables.  Start by making segment CD = y

 

Using the information, you get these two equations:

 

3x + 47 + y = 27 + x    and     y + 10 = x + 26

 

Next, combine like terms and put each expression in the same order:

 

2x + y = -20

-x + y =   16

 

Subtract the second equation from the first and you're left with:  3x = -36  therefore, x = -12

 

Now substitute the value for x into the equation for CE = x + 26 = -12 + 26 = 14

 

CE = 14    and incidentally, CD = 4