Question

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

A​ 10-gal aquarium is 4 in. higher than it is wide. Its length is 17 ​in., and its volume is 4284 in.^3. What are the height and width of the​ aquarium?

Answer 1

`W = 18` -- Width

`H = 14` --- Height

Explanation:

Given

`V = 4284` -- Volume

`L = 17` -- Length

`H = ??` -- Height

`W = 4 + H` -- Width

Required:

Find the height and the width

Volume is calculated as:

`V = LWH`

This gives:

`4284 = 17 * (4+H) * H`

`4284 = 17 * (4H+H^2)`

Open bracket

`4284 = 17 * 4H+17*H^2`

`4284 = 68H+17H^2`

Divide through by 17

`252 = 4H+H^2`

Write as a quadratic expression

`H^2 + 4H - 252 = 0`

Expand

`H^2 + 18H - 14H - 252 = 0`

Factorize:

`H(H + 18) - 14(H + 18) = 0`

Factor out H + 18

`(H - 14)(H + 18) = 0`

`H -14 = 0` or
`H + 18 = 0`

`H = 14` or
`H = -18`

But Height can not be negative. So:

`H = 14`

Recall that:

`W = 4 + H`

`W = 4 + 14`

`W = 18`