Answer:
Step-by-step explanation:
Given midsegment EF = (4x+6) and base segment BC = (9x+4) of a trapezoid with base AD = 3, you want the value of x and the lengths of the two segments EF and BC.
Midsegment
The midsegment parallel to the base segment is the average of the lengths of the parallel bases.
4x +6 = 1/2((9x +4) +3))
8x +12 = 9x +7 . . . . . . . . . multiply by 2 and simplify
5 = x . . . . . . . . . . . . subtract 8x+7
Segments
Using this value of x, we find the lengths of the segments to be ...
EF = 4·5 +6 = 26
BC = 9·5 +4 = 49
Check
(BC +AD)/2 = EF
(49 +3)/2 = 52/2 = 26 . . . . as required
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