Find the smallest pair of integer sided rectangles that fit the following criteria:
The first has three times the area of the second and
the second has three times the perimeter of the first.
Finding a good approach was harder than I expected. I eventually came up with this:
Let x be a side of the large perimeter rectangle.
Let y be a side of the large area rectangle.
Let s be the semiperimeter if the large area rectangle.
Then the other side of the large perimeter rectangle is 3s-x and the other side of the large area rectangle is s-y.
Then the areas create the equation y*(s-y) = 3*x*(3s-x). Solving for s yields s = (3x^2-y^2) / (9x-y).
Then it is just a matter of trying small x,y pairs. The smallest result occured for x=1 and y=15 yielding rectangles of 1x110 and 15x22.
Analytic Solution
