SOLUTION: a box with no top is to be formed from a rectangular cardboard by cutting 4cm squares from the corners and folding up the sides. the length of the box is to be 2cm more than its wi

Algebra ->  Rectangles -> SOLUTION: a box with no top is to be formed from a rectangular cardboard by cutting 4cm squares from the corners and folding up the sides. the length of the box is to be 2cm more than its wi      Log On


   

Question 1003752: a box with no top is to be formed from a rectangular cardboard by cutting 4cm squares from the corners and folding up the sides. the length of the box is to be 2cm more than its width and its volume is to be 252 cubic cm. find the dimensions of the sheet of the cardboard
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
volume = length * width * height

volume = 252

length * width * height = 252

your height will be 4 cm because you are cutting our 4 cm squares from each end and then folding up what is left.

your width is assumed to be x.

if your width is x, then your length has to be x + 2.

length * width * height = 252 becomes:

(x + 2) * x * 4 = 252

divide both sides of this equation by 4 to get:

(x + 2) * x = 63

simplify to get:

x^2 + 2x = 63

subtract 63 from both sides of this equation to get:

x^2 + 2x - 63 = 0

factor this quadratic equation to get:

(x + 9) * (x - 7) = 0

solve for x to get:

x = -9 or x = 7

x can't be negative, so you are left with x = 7

that's the width.

the length is equal to 2 + 2 which is equal to 9.

your box will have dimensions of:

length = 9
width = 7
height = 4

now you have to figure out what size paper you will need.

the length of your paper will have to be 9 cm + 4 cm on each end = 9 cm + 8 cm = 17 cm.

the width of your paper will have to be 7 cm + 4 cm on each end = 7 cm + 8 cm = 15 cm.

your paper will have to be 17 cm by 15 cm.

a picture of what your paper will look like after you marked it for cutting is shown below:

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