Answer:
Original Area : 48 square inches
Step-by-step explanation:
Let's say that the width of this rectangle is x, and the length of this rectangular is y. Remember that they are even consecutive integers as well, so let's make the length 2 greater than the width.
x = width,
x + 2 = length
And remember that the width decreases by 3 inches, to result in a rectangle of area 24. So the width will be x - 3, and the area will be (x - 3)(x + 2). Therefore we have the quadratic equation (x - 3)(x + 2) = 24, in which we can solve for x and y to determine the area of the original rectangle.
Step # 1 : Expand the expression (x - 3)(x + 2),
x² - x - 6 = 24
Step # 2 : Simplify and factor the expression x² - x - 6
x² - x - 30 = 0 ⇒ (x + 5)(x - 6) = 0
Step # 3 : Apply the Zero Factor Principle
x + 5 = 0, and x - 6 = 0
x = - 5, x = 6
Now remember that the width can't be negative, so it will be 6 inches long. That would make the length 6 + 2 = 8 inches. The area of the original rectangular will be 6 8 = 48 square inches.
