SOLUTION: A box with no top is to be constructed from a piece of cardboard whose width measures x in. and whose length measures 5 in. more than its width. The box is to be formed by cutting

Question 200637: A box with no top is to be constructed from a piece of cardboard whose width measures x in. and whose length measures 5 in. more than its width. The box is to be formed by cutting squares that measure 2 in. on each side from the four corners and then folding up the sides. If the volume of the box will be 72 in.3 what are the dimensions of the piece of cardboard?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A box with no top is to be constructed from a piece of cardboard whose width
measures x in. and whose length measures 5 in. more than its width.
The box is to be formed by cutting squares that measure 2 in. on each side
from the four corners and then folding up the sides.
If the volume of the box will be 72 in.3 what are the dimensions of the piece of cardboard?
:
Let x = the width of the cardboard
given
(x+5) = the length of the cardboard
Given
2" = the height of the box
:
(x-4) = width of the box
and
(x+5) - 4 =
(x+1) = length of the box
:
Volume equation
2*(x+1)*(x-4) = 72
FOIL
2(x^2 - 3x - 4) = 72
:
Divide both sides by 2
x^2 - 3x - 4 = 36
:
x^2 - 3x - 4 - 36 = 0
:
x^2 - 3x - 40 = 0
Factor
(x-8)(x+5) = 0
positive solution
x = 8
:
Cardboard: 13" by 8"
:
:
Check solution: find the vol of the box
(8+1) * (8-4) * 2 = 72
RELATED QUESTIONS
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)

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

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 9... (answered by ikleyn,Edwin McCravy)

A box with no top is to be constructed from a piece of cardboard whose length measures 10 (answered by ikleyn)

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

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

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