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Solve the problem. Check answers to be sure they are reasonable.

A 10-gallon aquarium is 4 inches higher than it is wide. Its length is 17 inches, and its volume is 4284 cubic inches. What are the height and width of the aquarium?

Answer :

Answer:

[tex]W = 18[/tex] -- Width

[tex]H = 14[/tex] --- Height

Step-by-step explanation:

Given

[tex]V = 4284[/tex] -- Volume

[tex]L = 17[/tex] -- Length

[tex]H = ??[/tex] -- Height

[tex]W = 4 + H[/tex] -- Width

Required:

Find the height and the width

Volume is calculated as:

[tex]V = LWH[/tex]

This gives:

[tex]4284 = 17 * (4+H) * H[/tex]

[tex]4284 = 17 * (4H+H^2)[/tex]

Open bracket

[tex]4284 = 17 * 4H+17*H^2[/tex]

[tex]4284 = 68H+17H^2[/tex]

Divide through by 17

[tex]252 = 4H+H^2[/tex]

Write as a quadratic expression

[tex]H^2 + 4H - 252 = 0[/tex]

Expand

[tex]H^2 + 18H - 14H - 252 = 0[/tex]

Factorize:

[tex]H(H + 18) - 14(H + 18) = 0[/tex]

Factor out H + 18

[tex](H - 14)(H + 18) = 0[/tex]

[tex]H -14 = 0[/tex] or [tex]H + 18 = 0[/tex]

[tex]H = 14[/tex] or [tex]H = -18[/tex]

But Height can not be negative. So:

[tex]H = 14[/tex]

Recall that:

[tex]W = 4 + H[/tex]

[tex]W = 4 + 14[/tex]

[tex]W = 18[/tex]

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