In the diagram below of triangle TUV, W is a midpoint of TU and X is a midpoint of UV. If WX=26−3x, and TV=5x+30, what is the measure of WX?
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Mid-point theorem states that when mid-points of two sides are joined, then the line joining the mid-points is parallel to the third side and its length is half the third side.
Using mid-point theorem,
WX = 1/2 × TY
=> (26-3x) = 1/2(5x+30)
=> 52 - 6x = 5x + 30
=> 11x = 22
=> x = 2
Therefore,
WX = 26-3x = 26-3×2 = 26 - 6 = 20.
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