The width of a rectangle is 2 inches less than its length. Find the length and width if the area of the rectangle is 35 inches wide.

x = length

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

Area = length x width

x(x - 2) = 35 {area is length x width}

x² - 2x = 35 {used distributive property}

x² - 2x - 35 = 0 {subtracted 35 from each side}

(x - 7)(x + 5) = 0 {factored into two binomials}

x - 7 = 0 or x + 5 = 0 {set each factor equal to 0}

x = 7 or x = -5 {solved each equation for x}

x = 7 {length cannot be negative}

x - 2 = 5 {substituted 7, in for x, into x - 2}

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

Area = length x width

x(x - 2) = 35 {area is length x width}

x² - 2x = 35 {used distributive property}

x² - 2x - 35 = 0 {subtracted 35 from each side}

(x - 7)(x + 5) = 0 {factored into two binomials}

x - 7 = 0 or x + 5 = 0 {set each factor equal to 0}

x = 7 or x = -5 {solved each equation for x}

x = 7 {length cannot be negative}

x - 2 = 5 {substituted 7, in for x, into x - 2}

**length is 7 in**. and**width is 5 in.****- Algebra House**