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 on the resulting rectangle is 99 square meters find the area of the original square
Let the original dimensions of the square be x meters each.
The area of the original square is x^2.
After the alterations:
One dimension is increased by 5 meters: x + 5
The other dimension is increased by 3 meters: x + 3
The area of the resulting rectangle is (x + 5)(x + 3) = 99
Expanding this equation, we get:
x^2 + 3x + 5x + 15 = 99
x^2 + 8x + 15 = 99
x^2 + 8x - 84 = 0
Solving this quadratic equation, we get:
(x + 14)(x - 6) = 0
Therefore, x = 6 or x = -14 (but x cannot be negative, so we ignore this solution)
Thus, the original dimensions of the square were each 6 meters.
The area of the original square is 6^2 = 36 square meters.