Question

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

Answer 1

Let the original side length of the square be x meters.

After increasing one dimension by 5 meters, the new length is x + 5 meters.
After increasing the other dimension by 3 meters, the new width is x + 3 meters.

The area of the resulting rectangle is (x + 5)(x + 3) = 99 square meters.

Expanding the expression, we get:
x^2 + 5x + 3x + 15 = 99
x^2 + 8x + 15 = 99
x^2 + 8x - 84 = 0

Factoring the quadratic equation, we get:
(x + 14)(x - 6) = 0

This gives us two possible solutions: x = -14 (which is not possible for a side length) and x = 6.

Therefore, the original side length of the square is 6 meters, and the area of the original square is:
Area = 6^2 = 36 square meters.