Question

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

Answer 1

Answer:

$W = 18$ -- Width

$H = 14$ --- Height

Step-by-step 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:

$W = 4 + H$

$W = 4 + 14$

$W = 18$