Dimensions of a photograph

The length of a photograph is 3 cm less than twice the width.  The area is 77cm².  Find the dimensions of the photograph.

x = width
2x - 3 = length   {length is 3 less than twice width}

Area of a rectangle is width x length

x(2x - 3) = 77   {area is width x length}
2x² - 3x = 77   {used distributive property}
2x² - 3x - 77 = 0   {subtracted 77 from both sides}
(2x + 11)(x - 7) = 0   {factored into two binomials}
2x + 11 = 0 or x - 7 = 0   {set each factor equal to 0}
2x = -11 or x = 7   {subtracted 11 and added 7}
x = -11/2 or x = 7   {divided first equation by 2}
x = 7   {width cannot be negative}
2x - 3 = 11   {substituted 7, in for x, into 2x - 3}

width = 7 cm
length = 11 cm 

Ask Algebra House