Volume of an aquarium

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.

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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

Ask Algebra House
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