In a small saucepan over medium-high heat, combine 1 cup sugar with 1 cup water and bring to a boil. Stir until the sugar is dissolved. Remove from the heat and cool to room temperature.
In a shallow bowl, mix together the remaining 1/4 cup sugar and salt. Set aside.
Using a lime wedge, moisten the rim of a margarita glass. Dip the moistened rim into the bowl of sugar-salt. Pour the margarita into the prepared glass. Slice the whole strawberries crosswise along its pointed end and place a strawberry onto the rim of each glass for garnish. Float 2 cucumber slices in the glass. Repeat with the remaining 3 margaritas.
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