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Question

The area of a trapezoidal field is 1400 square yards. Its altitude is 50 yards. Find the two bases, if the number of yards in each base is an integer divisible by 8. The number of solutions to this problem is:

Accepted Answer

Let us denote 8m and 8n to be our bases. Without loss of generality, let m n. Thus, 50 * 8m + 8n2 = 1400 4m + 4n = 28 m + n = 7 Since m & n are integers, we see that the only solutions to this equation are (1,6), (2,5), and (3,4). Therefore, the answer is three