SOLUTION: A box with no top is to be constructed from a piece of cardboard whose length measures 9 in. more than its width. The box is to be formed by cutting squares that measure 4 in. on e
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: A box with no top is to be constructed from a piece of cardboard whose length measures 9 in. more than its width. The box is to be formed by cutting squares that measure 4 in. on e
Log On
Question 1160912: A box with no top is to be constructed from a piece of cardboard whose length measures 9 in. more than its width. The box is to be formed by cutting squares that measure 4 in. on each side from the four corners and then folding up the sides. If the volume of the box will be 144 in.cubed​, what are the dimensions of the piece of​ cardboard? Found 2 solutions by ikleyn, Edwin McCravy:Answer by ikleyn(52781) (Show Source):
From the condition, the height of the box is 4 inches;
therefore, the area of its base is = 36 square inches.
If w is the width of the original cardboard in inches, then its length is (w+9) inches.
The dimensions of the base of the box are then (w-2*4) = (w-8) inches and (w+9-2*4) = (w+1) inches.
So you have this equation for the base area
(w-8)*(w+1) = 36.
Simplify and solve
w^2 - 8w + w - 8 = 36
w^2 - 7w - 44 = 0.
= = = .
Only positive root w = = 11 makes sense.
ANSWER. The original cardboard dimensions are 11 inches and 20 inches.
Here's the picture for Ikleyn's solution. She beat me posting.
The width is w, and the length is w+9 inches. We cut out the
4 green 4 in. by 4 in. squares at the corners and fold up the
sides and tape the edges to make an open-top box 4 inches high.
Edwin
