The volume of a rectangular box is 168cm³. It's length is one less than twice the width and the height is two more than the width. Suppose the width of the box is x.
Volume (lwh) - 168cm³
Width - w
Length - 2w - 1
Height - w + 2
[tex]V=LWH \\ 168cm³=(2w-1)(w)(w+2)[/tex]
✓ Simplify first the right side of the equation.
[tex]V=LWH \\ 168=(2w-1)(w)(w+2) \\ 168=(2w {}^{2} - w)(w + 2) \\ 168 = 2w {}^{3} + 4w {}^{2} - w {}^{2} - 2w \\ 168= 2w {}^{3} + 3w {}^{2} - 2w [/tex]
✓ Get the value of w (width) by simplifying the whole equation.
[tex]168 = 2w {}^{3} + 3w {}^{2} - 2w \\2w {}^{3} + 3w {}^{2} - 2w - 168 = 0 \\ 2w³-8w²+11w²-44w+42w-168=0\\2w²(x-4)+11w(x-4)+42(x-4)=0\\(x-4)(2w²+11w+42)=0\\\overline{x-4=0}\\(2w²+11w+42=0)\\\overline{w=4} \\ w \: \notin \:R[/tex]
✓ We already have the value of width which is 4. Then, substitute it to the given to find the other values.
[tex]Width: \\ w = \boxed4\\Length: \\ 2w - 1 = 2(4) - 1 = 8 - 1 = \boxed 7\\Height: \\ w + 2 = 4 + 2 = \boxed 6[/tex]
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a.4cm
b.5cm
c.6cm
d.7cm
a.4cm
b.5cm
c.6cm
d.7cm
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