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]
