Final answer:
The width of the framing material for a rectangular photograph can be found by subtracting the area of the photograph from the total combined area and dividing by the length of the photograph's longer side.
Step-by-step explanation:
Let's start by finding the area of the rectangular photograph. The formula for finding the area of a rectangle is length x width. In this case, the length is 7 inches and the width is 6 inches, so the area is 7 x 6 = 42 square inches.
Next, let's find the combined area of the photograph and the frame. We know that the total area is 156 square inches. So, if we subtract the area of the photograph (42 square inches) from the total area, we can find the area of the frame. 156 - 42 = 114 square inches.
Since the frame goes around the photograph on all four sides, we need to divide the area of the frame by the length of the photograph's longer side (7 inches) to find the width of the framing material. 114 / 7 = 16.28 inches.
So, the width of the framing material is approximately
16.28 inches
.