A farmer has two rectangular fields with a peculiar relationship. Both fields have integer dimensions. The corn field has three times the area of the hay field but the hay field has three times the perimeter.
It is also known that the dimensions of the corn field differ by 1, and the shorter dimension of the hay field is less than 100.
Find the dimensions of the two fields.
The solution states:
" a = 53*b +/- sqrt(9 + 2808*b^2)
Testing values of b less than 100, as specified in the problem, gives only one value of b: b=3.
If b=3 then a = 109 +/- 159, a = -50 or 318. Since a must be positive, a = 318. c then equals 53 "
But if b=3, then a = 159 +/- 159, so a = 0 or 318 => a = 318.
Despite the arithmetic typo, the solution that a = 318 is (magically!) correct.
Edited on June 19, 2007, 10:34 am
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