SOLUTION: I'm having trouble with setting up the equation of this word problem: A rectangle piece of cardboard is 5 cm longer than it is wide. A 3 cm square is cut out of each corner. The

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I'm having trouble with setting up the equation of this word problem: A rectangle piece of cardboard is 5 cm longer than it is wide. A 3 cm square is cut out of each corner. The      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1187292: I'm having trouble with setting up the equation of this word problem:
A rectangle piece of cardboard is 5 cm longer than it is wide. A 3 cm square is cut out of each corner. Then the four flaps are folded up to form a box without a lid. The volume of this box is 450 cubic cm. Find the length and width of the original piece of cardboard.
Thanks for the help!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the length L of rectangle piece of cardboard is 5cm} longer than it is wide,
L=W%2B5
after cutting 3cm (which will be the height of the box) square out of each corner,
L=W%2B5-6->L=W-1
W-6
the height h=3
Then the four flaps are folded up to form a box without a lid.
The volume of this box is V=450cm%5E3.
LWh=450cm%5E3
%28W-1%29%28W-6%29%2A3=450
3W%5E2+-+21+W+%2B+18=450
3W%5E2+-+21+W+%2B+18-450=0
3W%5E2+-+21+W+-432=0
W%5E2+-+7W+-144=0......using quadratic formula we get
W+=+-9
W+=16-> we need positive value for the width
then
L=16%2B5
L=21
the length and width of the original piece of cardboard are +21cm and 16cm respectively
proof:
%2821-6%29%2A%2816-6%29%2A3=450
450=450