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

Algebra ->  Coordinate Systems and Linear Equations -> 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       Log On


   

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) About Me  (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