SOLUTION: Hi, Thank you for answering my question in advance. My question is: A rectangular sheet of brass is twice as long as it is wide. Squares 3cmx3cm are cut from each corner, a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi, Thank you for answering my question in advance. My question is: A rectangular sheet of brass is twice as long as it is wide. Squares 3cmx3cm are cut from each corner, a      Log On


   

Question 1010952: Hi,
Thank you for answering my question in advance.
My question is:
A rectangular sheet of brass is twice as long as it is wide. Squares 3cmx3cm are cut from each corner, and the ends are turned up to form an open box having a volume of 648cm^3. What are the dimensions of the original sheet of brass.

Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L=2w, and w are the original brass sheet dimensions.
volume will be 3%28L-2%2A3%29%28w-2%2A3%29=648

Substitute for L.
3%282w-6%29%28w-6%29=648
Simplify.
%282w-6%29%28w-6%29=216
2%28w-3%29%28w-6%29=216
%28w-3%29%28w-6%29=108
w%5E2-9w%2B18-108=0
w%5E2-9w-90=0
General solution formula for quadratic equation gives
w=%289%2B-+sqrt%28441%29%29%2F2
w=%289%2B-+21%29%2F2
Take the PLUS form.
w=%289%2B21%29%2F2
highlight%28w=15%29

highlight%28L=30%29