SOLUTION: A ten-gallon aquarium is 3 inches higher than it is wide. Its length is 21 inches., and its volume is 2730 inches cubed. What are the height and width of the aquarium?

Question 4460: A ten-gallon aquarium is 3 inches higher than it is wide. Its length is 21 inches., and its volume is 2730 inches cubed. What are the height and width of the aquarium?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Start with the formula for the volume of a rectangular prism (this is the shape of the aquarium): V = L*W*H (That's Length * Width * Height)
L = 21 inches
H = W + 3
V = (21)(W)(W+3) = 2730 cubic inches.
(21)(W^2 + 3W) = 2730 Cubic inches. Divide both sides by 21.
W^2 + 3W = 130 Subtract 130 from both sides.
W^2 + 3W - 130 = 0 Solve the quadratic by factoring.
(W + 13)(W - 10) = 0 Apply the zero products principle.
W + 13 = 0, W = -13 Discard this solution as negative width is not meaningful.
W - 10 = 0, W = 10 The width of the aquarium is 10 inches.
H = W + 3
H = 13 The height of the aquarium is 13 inches.
Check: Volume, V = (21")(10")(13") = 2730 cubic inches.
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