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Question

The perimeter of an equilateral triangle exceeds the perimeter of a square by 1989 cm. The length of each side of the triangle exceeds the length of each side of the square by d cm. The square has perimeter greater than 0. How many positive integers are NOT possible value for d?

Accepted Answer

If t is the side of the triangle, and s is the side of the square, then 3t-4s=1989 t-s=d Solving the first equation for t gives t = 4s+19893 Substituting into the second equation, 4s+19893 - s = d s+19893 = d s+1989 = 3d If s = 0, d = 663. But s has to be greater than 0, so the first 663 positive integers aren't possible 663