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
2 answers:
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
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