Larry P.

# Please, give an appropriate mathematical statement for the following problem

An open box is to be formed out of a rectangle piece of cardboard whose length is 12cm longer than its width. To form the box, a square of side 5 cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up. If the box was to hold at most 1900 cm^3, what mathematical statement would represent the given situation?

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Michael P.

I should not have sent this solution in!  Sorry- too early!

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02/20/18

Michael P.

Looking at the problem again, I was focused on the solving the cardboard dimensions but it is still screwed up

v = x*w*h =1900

where: x = length of box (cm)
w = width of box (cm) = x - 12 cm
h = height of box = 5 cm

therefore, v = x*(l-12)*h = 1900
x^2 - 12*x= 1900/h = 380

Put in standard quadratic form:   a*x^2 + b*x + c = 0

x^2 - 12*x - 380 =0           where:  a = 1     b = -12     c = -380

and solve for positive root, x:   x = [12 + √(144 + 4*380)]/2  = 26.4 cm length of box

w = x - 12 cm = 26.4 cm - 12 cm = 14.4 cm width of box

checking volume of box = x*w*h = (26.4 cm)*(14.4 cm)*5 cm = 1900.8 cm^3    I rounded up with length so am > 1900 cm^3 but it is approximate
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02/20/18

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