If one side of a square is increased by 2 inches and an adjacent side is decreased by 2 inches, the area of the resulting rectangle is 32 square inches. Find the length of one side of the square.
(x+2)(x-2) = 32
x^2 - 4 = 32
x^2 = 36
x = ±6 , but x is a side of a square so it must be positive
x = 6
The original square was 6 by 6
the new square is 4 by 8
and 4(8) = 32, answer is correct
To solve this problem, let's call the length of one side of the square x inches.
According to the problem, when one side of the square is increased by 2 inches, it becomes x + 2 inches. And when an adjacent side is decreased by 2 inches, it becomes x - 2 inches.
The area of a rectangle is given by multiplying its length by its width. In this case, the length of the resulting rectangle is x + 2 inches and the width is x - 2 inches. Therefore, the area of the resulting rectangle is (x + 2)(x - 2) = 32 square inches.
Expanding the equation, we get x² - 4 = 32.
Next, let's solve this quadratic equation:
x² - 4 = 32
x² = 36
x = ± √36
x = ±6
Since the length of the side of a square cannot be negative, we can conclude that x = 6 inches.
Therefore, the length of one side of the square is 6 inches.