# Problem of the Day: 1/2/13

How many rectangles have an area that is a perfect square between 1 and 100, inclusive, but have unequal but integral dimensions?

Solution to yesterday’s problem:

The difference of two squares factors out to the sum and difference of their roots, as you can see below when FOILing:

$(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2$

So $2013^2-2010^2$ factors to $(2013+2010)(2013-2010)$.

Simplifying, $4023\times3$. Therefore the answer is 12,069.