Question 884751: A rectangular sheet of metal is 30 in by 40 in. An open rectangular box is made by cutting squares of equal areas from the four corners and folding up the ends. if the area of the base of the box is 336 inches square, find the total area of the discarded squares
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular sheet of metal is 30 in by 40 in.
An open rectangular box is made by cutting squares of equal areas from the four corners and folding up the ends.
if the area of the base of the box is 336 inches square, find the total area of the discarded squares.\
:
Let x = length of the side of one of the squares, also the height of the box
then
x^2 = area of one of the squares
and
4x^2 = the total area of the 4 squares
:
If the area of the base is 336 then the volume of the box = 336x cu in
:
the dimensions of the box:
(30-2x) by (40-2x) by x
:
The volume equation
(30-2x)(40-2x)*x = 336x
Divide both sides by x
(30-2x)(40-2x) = 336
FOIL
1200 - 60x - 80x + 4x^2 = 336
Form a quadratic equation
4x^2 - 140x + 1200 - 336 = 0
4x^2 - 140x + 864 = 0
simplify, divide by 4
x^2 - 35x + 216 = 0
you can use the quadratic formula, but this will factor
x = 27
x = 8; this is only solution that will make sense
then
4(8^2) = 512 sq/in is the area of the removed squares
:
:
Check this, find the area of the base by subtracting 2x (16), from 40 and 30
14 * 24 = 336
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