An aquarium holding African cichlids is 4 inches higher than it is wide. Its length is 29 inches, and its volume is 4060 in.³ Find the width and the height of the aquarium.

**w = width**

w + 4 = height

29 = length

w + 4 = height

29 = length

**Volume of an aquarium (rectangular prism)**

V = lwh{volume = length x width x height}

V = lwh

29(w)(w + 4) = 4060 {substituted into volume formula}

w(w + 4) = 140 {divided each side by 29}

w² + 4w = 140 {used distributive property}

w² + 4w - 140 = 0 {subtracted 140 from each side}

(w + 14)(w - 10) = 0 {factored into two binomials}

w + 14 = 0 or w - 10 = 0 {set each factor equal to 0}

w = -14 or w = 10 {solved each equation for w}

w = 10 only {width of an aquarium cannot be negative}

w + 4 = 14 {substituted 10, in for w, into w + 4}

**width = 10 inches**

height = 14 inches

length = 29 inches

height = 14 inches

length = 29 inches

*- Algebra House*