The measures of the sides of a rectangle are even numbers. How many rectangles of this type exist with an area equal to 96?
If $a$ and $b$ denote the length and width of the rectangle, we have $a \times b=96$. Therefore, $a$ and $b$ are even divisors of 96, and thus we have four rectangles satisfying the given conditions, namely, rectangles with sides measuring 2 and 48; 4 and $24 ; 6$ and 16 and 8 and 12.