a sheet of steel has an area of 1200 cm2 6 cm squares are cu

a sheet of steel has an area of 1200 cm^2. 6 cm squares are cut from each corner and the edges folded up to to form a box with a volume of 3456 cm^3. What are the dimensions of the box? Use the substitution or elimination method.

Solution

Let the sheet of steel has the dimension length L and the width W.

The Area A= LW = 1200 cm² => L = 1200/W
When we cut 6-cm squares from each corner of the sheet and fold up then the formed box will have the dimensions length (L-12), width (W-12) and height of 6
then volume, V = 6(L-12)(W-12) = 6(1200/W - 12)(W-12) = 6(1344 - 14400/W - 12W)
Given V= 3456 cm³
so, 6(1344 - 14400/W - 12W) = 3456
=> 1344 - 14400/W - 12W = 576
=> 768 - 14400/W - 12W = 0
=> 768W - 14400 - 12W² = 0
=>12W² - 768W + 14400 = 0
=>W² - 64W +1200 = 0
After finding the roots we get the imaginary roots.that is theree is no real solutions.

We know that for maximum volume when sheet is square, so the length and width will be 203 cm.

With this dimensionwe get the is 3075.69 cm³.

Hence we can\'t get the sheet of steel which have the volume of 3456 cm³