A box with no top is to be constructed from a piece of cardboard whose length measures 13in. more than its width. The box is to be formed by cutting squares that measure 4in. on each side from the four corners and then folding up the sides. If the volume of the box will be 456in.3​,what are the dimensions of the piece of​ cardboard?

Question
Asked Nov 23, 2019
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A box with no top is to be constructed from a piece of cardboard whose length measures 13in. more than its width. The box is to be formed by cutting squares that measure 4in. on each side from the four corners and then folding up the sides. If the volume of the box will be 456in.3​,
what are the dimensions of the piece of​ cardboard?
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Expert Answer

Step 1

Let x inches be the width of the cardboard, then the length is (x + 13) inches, because length is 13 inches more than the width.

 

Step 2

After cutting four squares from each corner that measures 4 inches, the width, length and height are

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width x-8 Length x+13-8=x+5 height 4 inches

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Step 3

Now the volume of ...

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volume length x width x height (x+5) (x-8)-4= 456 4(x-3x-40) 456 4x 12x616 = 0 -3x-154=0 (dividing by 4 on sides)

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Math

Algebra

Polynomials