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.
Corn field is 53 x 54. Hay field is 318 x 3.
If the corn field is a x b and the hay field is c x d, then:
ab = 3cd
3(a + b) = c + d
a = b + 1
Substituting for a and then b, we get
c**2 - 106cd + d**2 - 9 = 0
Not sure how you might solve this, but d = 3 seemed a good idea, and turned out to work.
Solution
