Final answer:
To determine the dimensions of Tonya's rug, we set up a quadratic equation based on the area and the relationship between length and width, solved for the width, and then found the length. The width is 6 feet, and the length is 9 feet.
Step-by-step explanation:
Tonya has a rectangular rug with an area of 54 square feet. To find the length and width of the rug, we need to set up an equation using the given that the rug is 3 feet longer than it is wide. Let w represent the width of the rug in feet. Therefore, the length of the rug will be w + 3 feet. Since area is calculated as length times width, the equation to represent the area of the rug is w times (w + 3) = 54.
Now we solve the quadratic equation:
w2 + 3w = 54.
We subtract 54 from both sides to set the equation to zero: w2 + 3w - 54 = 0. This equation factors to (w + 9)(w - 6) = 0. Therefore, w can be either -9 or 6. Since a width cannot be negative, the width must be 6 feet, and the length is 6 + 3 = 9 feet.
So, the dimensions of Tonya's rug are 6 feet wide and 9 feet long.