A photograph has a length that is 6 inches longer than its width, x. So its area is given by the expression x(x + 6) square inches. If the area of the photograph is 112 square inches, what is the width of the photograph?
We are given the area of the photograph as x(x + 6) square inches. We are also told that the area of the photograph is 112 square inches. So we can set up the equation x(x + 6) = 112.
Expanding the expression on the left side of the equation, we get x² + 6x = 112. Rearranging this equation, we have x² + 6x - 112 = 0.
Now, we can factor this quadratic equation. The factors of -112 that add up to 6 are 14 and -8. So the equation can be factored as (x + 14)(x - 8) = 0.
Setting each factor equal to zero, we have x + 14 = 0 or x - 8 = 0. Solving these equations, we find that x = -14 or x = 8.
Since the width cannot be negative, we discard x = -14 as an extraneous root. Thus, the width of the photograph is x = 8 inches.