Final answer:
To solve for the original area of the square room, we must set up an equation based on the altered dimensions of the resulting rectangular room. By applying algebraic methods, we can find the value of x, which represents the side length of the original square, and then calculate the original area as x^2.
Step-by-step explanation:
To find the original area of a square-shaped room after its dimensions have been altered to create a rectangular-shaped room, we can set up an equation. Let x represent the length of a side of the original square room. When altered, one wall is increased by 9 feet, making the length x + 9 feet, and the other wall is decreased by 4 feet, making the width x - 4 feet. The area of the resulting rectangle is given as 90 square feet, so we have:
(x + 9)(x - 4) = 90
Expanding this and setting it equal to 90, we get:
x2 + 5x - 36 = 90
Subtracting 90 from both sides:
x2 + 5x - 126 = 0
Factoring, we get two possible solutions for x, but since a physical room cannot have negative dimensions, we choose the positive solution. Once we find the value of x, the original area of the square room is simply x2.