The figure shown above represents a modern painting…
We are given a painting that has 4 different colored rectangles, each with a length of l and a width of w. We are also given that the entire painting has an area of 4,800 square inches. Let’s begin by sketching the given diagram. We can also add in the appropriate dimensions to each side.
From the diagram we can create an equation:
l = w + w + w
We also know that the area is 4,800 square inches. Using the dimensions from our diagram and the formula for the area of a rectangle, we can say:
l(w + l) = 4,800
Since l = 3w, we can substitute 3w for l in the area equation l(w + l) = 4,800. Thus, we have:
3w(w + 3w) = 4,800
3w(4w) = 4,800
12w^2 = 4,800
w^2 = 400
w = ±20
Because we are dealing with a measurement, we disregard w = -20 as a solution. Thus, the width of each rectangle is 20 inches.