I came across the following problem and I know for certain the answer is $6$, but am unsure as to where this comes from.
Let $m$ be the sum of the digits in 4950. The difference in the area of two similar triangles is $m$ square feet, and the ratio of the larger area to the smaller area is the square of an integer. The area of the smaller triangle, in square feet, is an integer and one of its sides is $3$ feet. Find the length of the corresponding side of the larger triangle in feet.
Besides the obvious fact that $m=18$. I am unsure as to how to approach this problem.