Problema Solution
A box with no top is to be constructed from a piece of cardboard whose length measure 8in. more then its width. The box is formed by cutting squares that measure 3in. on each side from the four corners and then folding up the sides. If the volume of the box will be 27 cubic inches, what are the dimensions of the piece of cardboard. What is the length? What is the width?
Answer provided by our tutors
let
l = the length of the rectangular piece of cardboard, l>0
w = the width of the rectangular piece of cardboard, w>0
s = 3 in
the length measures 8 in more then its width
l = 8 + w
the volume of the box will be 27 cubic inches
(l - 2*3)(w - 2*3)*3 = 27 divide both sides by 3
(l - 6)(w - 6) = 9
plug l = 8 + w into the last equation
(8 + w - 6)(w - 6) = 9
by solving we find
w = 7 in
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l = 8 + 7
l = 15 in
the length is 15 inches.
the width is 7 inches.