In triangle PQR, sides PQ and QR have lengths 5 and 11, respectively. Triangle PQR has the same perimieter as equilateral triangle STU. If the lengths of side ST is an integer, which of the following could be the length of side PR?

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You have not listed the possible lengths, but we can eliminate some integers: 1 through 5. Let x be the length of side PR 16 + x is the perimeter of triangle PQR Triangle STU is equilateral so let its sides be Y and Y must be an integer. 16 + x = 3Y x = 3Y -16 Y must therefore be  6 or larger because a negative length does not make sense.