A rectangular piece of sheet metal is 6 inches shorter than it is wide. From each corner, a 0.5 x 0.5 inch square is cut out and the flaps are then folded up to form an open box. You are given that volume of the open box is 1736 in3.
What is the length?
What is the width?
?
Favorite Answer
Length => w - 6
Width => w
With 0.5 cut off both ends we have:
Length => w - 6 - 2(0.5)
Width => w - 2(0.5)
Hence, Length = w - 7 and width w - 1
As the height is 0.5 and volume is l x w x h we have:
Volume = 0.5(w - 7)(w - 1) = 1736
i.e. (w - 7)(w - 1) = 3472
or, w² - 8w - 3465 = 0
so, (w - 63)(w + 55) = 0
Hence, w = 63 or -55...not possible
With w = 63, l = 57....rectangular sheet
If 0.5 is cut from both ends we have a tray that is 62 wide by 56 in length and 0.5 high
so, 0.5 x 62 x 56 => 1736...correct
:)>
Bryce
V= L*W*H
W= L - 61736= 0.5(L - 1)(L - 7)
3472= L² - 8L + 7
L² - 8L - 3465= 0
L= 63 in, W= 57 in