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?

Question

The width of the photograph is blank inches.

The solution is

Answer 1

To find the width of the photograph, we can set up the equation:

x(x + 6) = 112

Expanding the left side of the equation, we get:

x^2 + 6x = 112

Rearranging this equation into standard form, we get:

x^2 + 6x - 112 = 0

Now we can factor this quadratic equation:

(x + 14)(x - 8) = 0

Setting each factor to zero, we find two possible values for x:

x + 14 = 0
x = -14 (This is not a valid solution for the width of a photograph)

x - 8 = 0
x = 8

Therefore, the width of the photograph is 8 inches.