Answer :
h = 7
l = w + 6
V = 280
V = lwh
Plug in what we know:
280 = (w + 6)(w)(7)
Distribute W into the first parenthesis:
280 = (w^2 + 6w)(7)
Distribute 7:
280 = 7w^2 + 42w
Divide 7 to both sides:
40 = w^2 + 6w
Subtract 40 to both sides:
w^2 + 6w - 40 = 0
Factor:
(w - 4)(w + 10) = 0
Therefore, w = 4.
Plug this back into the equation for the length:
l = w + 6
l = 4 + 6
l = 10
l = w + 6
V = 280
V = lwh
Plug in what we know:
280 = (w + 6)(w)(7)
Distribute W into the first parenthesis:
280 = (w^2 + 6w)(7)
Distribute 7:
280 = 7w^2 + 42w
Divide 7 to both sides:
40 = w^2 + 6w
Subtract 40 to both sides:
w^2 + 6w - 40 = 0
Factor:
(w - 4)(w + 10) = 0
Therefore, w = 4.
Plug this back into the equation for the length:
l = w + 6
l = 4 + 6
l = 10
[tex]Volume=Length*Width*Height \\ 280=(x+6)*x*7 \\ 280=7x(x+6) \\ 280=7x^{2}+42x \\ 0=7x^{2}+42x-280 \\ 0=7(x^{2}+6x-40) \\ 0=7(x+10)(x-4) \\ Since\ we\ can't\ have\ negative\ values,\ x=4 \\ Width=4 \\ Length=Width+6 \\ Length=4+6 \\ \boxed{Length=10}[/tex]
