Since triangle TUV is similar to triangle WXY, the corresponding sides are proportional. The ratio of TU to WX is the same as the ratio of TV to WY. Given TU = 2, TV = 3, and WX = 12.6, we can set up the proportion:
2 / 12.6 = 3 / YW
Cross-multiply to solve for YW:
2 * YW = 3 * 12.6
YW = (3 * 12.6) / 2
YW = 37.8 / 2
YW = 18.9
Therefore, the measure of side YW is 18.9.
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