precalc please help!!
posted by steph .
an open box with a volume of 1500cm cubed is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. show that this can be done in two ways, and find exact dimensions of the box in each case.

Cutting an xcm notch from each corner of the sheet, leaves a box (202x)x(402x). We want that volume to be 1500.
(202x)(402x) = 1500
4x^2  120x  700 = 0
x = 5 or 35
so, a 30x50 box will fit the bill
The solution x=35 produces a box of negative dimensions.
Respond to this Question
Similar Questions

PRECALCULUS
AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF CARDBOARD THAT IS 16 FT BY 19 FT AND FOLDING UP THE FLAPS. WHAT SIZE CORNER SQUARES SHOULD BE CUT TO YEILD A BOX THAT HAS A VOLUME OF 175 CUBIC FEET 
math
a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard. … 
calc
by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the … 
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 volume … 
math
An open box is made from a rectangular piece of cardboard, with dimensions of 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. Determine the dimensions of the squares to be cut to create a box … 
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 … 
PreCalc
An open box with a volume of 1500cm^3 is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. Show that this can be done in two different … 
precalc
A box with an open top is to be constructed by cutting equalsized squares out of the corners of a 18 inch by 30 inch piece of cardboard and folding up the sides. a) Let w be the length of the sides of the cut out squares. Determine … 
Calculus 1
A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume … 
Pre Calculus
A piece of cardboard measuring 13 inches by 11 inches is formed into an opentop box by cutting squares with side length x from each corner and folding up the sides. a. Find a formula for the volume of the box in terms of x b. Find …