SOLUTION: A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the

Algebra ->  Volume -> SOLUTION: A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the       Log On


   

Question 1050782: A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 644 in^3​, what were the original dimensions of the piece of​ metal?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the net and label all of the parts.
Length, L
Width , w
1 inch square removed at each corner;
Dimensions for the base formed when flaps folded up, (L-2*1) and (w-2*1).
1, ALSO the "height" of the box.

What else is given?
highlight%28L=w%2B5%29.

Equation showing volume:
1%2A%28L-2%29%28w-2%29=644
%28L-2%29%28w-2%29=644
Substitution for L:
%28w%2B5-2%29%28w-2%29=644
highlight%28%28w%2B3%29%28w-2%29=644%29

The rest is arithmetic of Intermediate Algebra level quadratic equation skills. The longer part, for some people, is to do the analysis leading to the quadratic equation to be solved.