The second order polynomial that involves the variable x (border inside the rectangle) and associated to the unshaded area is x² - 62 · x + 232 = 0.
How to derive an expression for the area of an unshaded region of a rectangle
The area of a rectangle (A), in square inches, is equal to the product of its width (w), in inches, and its height (h), in inches. According to the figure, we have two proportional rectangles and we need to derive an expression that describes the value of the unshaded area.
If we know that A = 648 in², w = 22 - x and h = 40 - x, then the expression is derived below:
A = w · h
(22 - x) · (40 - x) = 648
40 · (22 - x) - x · (22 - x) = 648
880 - 40 · x - 22 · x + x² = 648
x² - 62 · x + 232 = 0
The second order polynomial that involves the variable x (border inside the rectangle) and associated to the unshaded area is x² - 62 · x + 232 = 0. [tex]\blacksquare[/tex]
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