Final answer:
The dimensions of Jimmy's family's deck are solved by setting up a quadratic equation based on the given area and the relationship between the length and the width. By factoring the equation W^2 + 7W - 144 = 0, we find that the width is 9 feet, and thus the length is 16 feet.
Step-by-step explanation:
Jimmy's family has a rectangular deck that is 7 feet longer than it is wide. If the area of the deck is 144 square feet, what are the dimensions of the deck? To solve for the dimensions, let's let the width of the deck be W feet and therefore the length is W + 7 feet. Since the area of a rectangle is found by multiplying the length and width together, we can write the equation as W * (W + 7) = 144 square feet.
Step 1: Set up the equation W(W + 7) = 144.
Step 2: Expand the equation to W^2 + 7W = 144.
Step 3: Rearrange into a quadratic equation W^2 + 7W - 144 = 0.
Step 4: Factor the quadratic equation to find the values of W.
Step 5: Solve the factors to find the width W, and then find the length by adding 7 to the width.
Using the factoring method or the quadratic formula, we can determine that the dimensions of the deck are 9 feet in width and 16 feet in length (since W^2 + 7W - 144 = (W - 9)(W + 16), thus W = 9).