# Algebra

A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding up the sides. If the volume of the box will be 110 inches cubed what are the dimensions of the piece of cardboard?

1. 👍
2. 👎
3. 👁
1. Let x = width of cardboard
Therefore L = x+6
volume of open box is 110 in^3
cut squares are 2 inches = H

V=HXWxL=110
H=2
W=x-4
L=(x+6)-4

2(x-4)(x+2)=110 ==> divide both sides by 2

(x-4)(x+2)=55
x^2 -2x -8 = 55 ==> subtract 55 from both sides

X^2 -2x -63 = 0 ==> factor

(x-9)(x+7) = 0
x= 9 or -7 ==> x has to be greater than 0, therefore answer is 9

check

2((9)-4)((9)+6-4)=110
2(5)(11)=110
110=110 it checks

dimensions of cardboard is
W=9 inches
L=(9)+6=15 inches

1. 👍
2. 👎

## Similar Questions

1. ### calculus

An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box. (a) Express the volume V of the box as a

2. ### math

an open rectangular box is to be formed by cutting identical squares, each of side 2 in, one from each corner of a rectangular piece of cardboard, and then turning up the ends. If the area of the piece of cardboard is 160 in² and

3. ### math

an open box is to be formed out of a rectangular piece of cardboard whose length is 8 cm longer than its width to form the box,a square of side 4 cm will be removed from each corner of the cardboard then the edges of the remaining

4. ### math

A square piece of cardboard is to be used to form a box without a top by cutting off squares, 5cm on a side, from each corner and then folding up the sides. if the volume of the box must be 320 sq. sm, what must be the length of a

1. ### Math

A rectangular piece of cardboard measuring 12 cm by 18 cm is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each square in

2. ### Math

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in by 12 in by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the

3. ### math

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 324 in3. How big a piece of

4. ### Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box

1. ### Calculus

A cardboard box of 32in^3 volume with a square base and open top is to be constructed. What is the length of base that will minimize the surface area?

2. ### AP Calculus

A cardboard box of 108in cubed volume with a square base and no top constructed. Find the minimum area of the cardboard needed. (Optimization)

3. ### Math HELP!!

Chuck needs to cut a piece of cardboard for an art project at school. He has four pieces of cardboard that he can cut from: 6 inches, 5 inches, 7 inches, and 3 inches. If the length of the cardboard he needs is √35 inches, which

4. ### Calculus

an open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning up the sides. If the piece of cardboard is 12 cm by 24 cm, what are the dimensions of the box that has the largest