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
- Algebra House
