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
Volume of an aquarium (rectangular prism)
V = lwh {volume = length x width x height}
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
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w + 4 = height
29 = length
Volume of an aquarium (rectangular prism)
V = lwh {volume = length x width x height}
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
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