A square is altered so that one dimension is increased by 5 meters and the other dimension is increased by 3 meters. If the area of the resulting rectangle is 99 square meters, find the area of the original square.
Let the original side length of the square be x meters.
After altering the square, the new dimensions of the rectangle are x + 5 meters and x + 3 meters.
The area of the new rectangle is given by (x + 5)(x + 3) = 99.
Expanding this equation, we get x^2 + 8x + 15 = 99.
Rearranging the terms, we get x^2 + 8x - 84 = 0.
Solving this quadratic equation, we find that x = 6 or x = -14, but since the side length of a square cannot be negative, the original side length of the square is 6 meters.
Therefore, the area of the original square is 6^2 = 36 square meters.