precalc please help!!
posted by steph on .
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.