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

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) (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:

$$$

RELATED QUESTIONS
A box with no top is to be formed from a rectangular cardboard by cutting 4 cm squares... (answered by ankor@dixie-net.com)

A box with an open top is formed by cutting squares out of the corners of a rectangular... (answered by Earlsdon)

A box with no top is to be constructed from a piece of cardboard whose width measures x... (answered by ankor@dixie-net.com)

Please help me solve this problem: A box with no top is to be constructed from a piece of (answered by josmiceli)

Please help me solve this: A box with no top is to be constructed from a piece of... (answered by josgarithmetic,MathTherapy)

please help solve a box with no top is to be constructed from a piece of cardboard... (answered by venugopalramana)

A box with no top is to be constructed from a piece of cardboard whose length measures 9... (answered by ikleyn,Edwin McCravy)

A box with no top is to be constructed from a piece of cardboard whose length measures 12 (answered by josmiceli)

A box with no top is to be constructed from a piece of cardboard whose length measures 12 (answered by TimothyLamb)