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The measure of length of GF is 16 cm.
Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:
We are given the following;
FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]
GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]
ST = 8 cm
Substitute the given values, we will get the following;
GF = 2 * 8 = 16 cm
Thus, the measure of the length of GF is 16 cm.
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