# If EF=12, IJ=3x-4, andHG=x, find lengths IJ and HG. I know I have to use the midsegment theorem for trapezoids but the 3x-4 is throwing me off(Picture link below)...

If EF=12, IJ=3x-4, andHG=x, find lengths IJ and HG.

I know I have to use the midsegment theorem for trapezoids but the 3x-4 is throwing me off(Picture link below)

http://static.panoramio.com/photos/medium/89653620.jpg

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Expert Answers

durbanville | Certified Educator

In the diagram EF (12) and HG (x) are the bases of the trapezoid. IJ (3x-4) is the median or mid-segment line. The theorem states that the mid-segment (IJ) is equal to half of the sum of the bases (EF and HG)

`IJ=1/2 (EF +HG)` To apply that using the values we have:

`therefore3x-4 = 1/2(12+x)`

Now solve remembering to distribute the 1/2 between 12 AND x

`3x-4= 6 +1/2x`

`therefore 3x-1/2x = 6+4`

`therefore 5/2x=10`

`therefore 5x= 20`

`therefore x= 20/5 = 4`

So, if HG = x = 4

and IJ=3x-4 = 3(4)-4

IJ = 8

**Ans. HG=4 and IJ=8**

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