Question

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?

Answer 1

112 = x(x + 6)
112 = x^2 + 6x
x^2 + 6x - 112 = 0
(x - 8)(x + 14) = 0

x - 8 = 0
x = 8

x + 14 = 0
x = -14....not this one because it is negative

x = 8 <===width = 8 inches

L = x + 6
L = 8 + 6
L = 14 ....length = 14

Answer 2

The width of the photograph is 8 inches

let

width of the photograph = x

length of the photograph = 6 + x

Area  = x(6 + x)

112 =  x(6 + x)

112 = 6x + x²

x² + 6x - 112 = 0

x² - 8x + 14x - 112 = 0

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

(x + 14)(x - 8)

x = -14 or 8

x = 8

x cannot be negative so we use only 8.

width of the photograph = 8 inches

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