Homework Help: pre-calc please help!!

Posted by steph on Thursday, November 10, 2011 at 9:52pm.

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.

pre-calc please help!! - Steve, Friday, November 11, 2011 at 10:43am
Cutting an x-cm notch from each corner of the sheet, leaves a box (20-2x)x(40-2x). We want that volume to be 1500.

(20-2x)(40-2x) = 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.

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