Answered

The height of a box is 7 inches. Its length is 6 inches more than its width. Find the length if the volume is 280

cubic inches.

Verified Answer :

iGreen

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

dln

\(Volume=Length*Width*Height \\ 280=(x+6)*x*7 \\ 280=7x(x+6) \\ 280=7x^{2}+42x \\ 0=7x^{2}+42x-280 \\ 0=7(x^{2}+6x-40) \\ 0=7(x+10)(x-4) \\ Since\ we\ can't\ have\ negative\ values,\ x=4 \\ Width=4 \\ Length=Width+6 \\ Length=4+6 \\ \boxed{Length=10}\)

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