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If EF=12, IJ=3x-4, andHG=x, find lengths IJ and HG. I know I have to use the midsegment...
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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 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
Posted by durbanville on May 2, 2013 at 10:45 AM (Answer #1)
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