The smaller rectangle in the figure above…
We are given a diagram, which represents a parking lot, with a smaller rectangle inside a larger rectangle. The dimensions of the smaller rectangle are 100 ft by 150 ft, and the dimensions of the larger rectangle are (100 + w) ft by (150 + w) ft. Since the area of the larger rectangle is twice that of the smaller rectangle, we can create the following equation:
(w + 100)(w + 150) = 2(100 x 150)
w^2 + 250w + 15,000 = 30,000
w^2 + 250w – 15,000 = 0
(w + 300)(w – 50) = 0
w = -300 or w = 50
Since w must be positive, w must be 50.