Final answer:
The dimensions of Aladdin's magic carpet are 9 yards in width and 12 yards in length. This was determined by setting up a quadratic equation from given area and the relation between length and width, solving for the width, and then finding the length.
Step-by-step explanation:
To determine the dimensions of Aladdin's magic carpet given the information that the carpet is rectangular, has a length 3 yards more than its width, and the area of the carpet is 108 sq yards, we can set up an algebraic equation.
The area A of a rectangle is given by the product of its length L and width W, so:
A = L * W
From the question:
L = W + 3
A = 108 sq yards
Substitute the expression for L into the area equation:
108 = (W + 3) * W
Solve this quadratic equation by expanding and rearranging terms:
W2 + 3W - 108 = 0
Factor the quadratic equation:
(W + 12)(W - 9) = 0
Set each factor equal to zero and solve for W:
W + 12 = 0 or W - 9 = 0
W = -12 (reject because width cannot be negative) or W = 9
Since W is the width, we now know it is 9 yards. Next, calculate the length:
L = W + 3
L = 9 + 3
L = 12 yards
Thus, the dimensions of the magic carpet are 9 yards in width and 12 yards in length.