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.

Answer 1

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.