SOLUTION: a rectangular piece of cardboard has a length that is 3 inches longer than the width. A square 1.5 inches on a side is cut from each corner. the sides are then turned up to form an

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a rectangular piece of cardboard has a length that is 3 inches longer than the width. A square 1.5 inches on a side is cut from each corner. the sides are then turned up to form an      Log On


   

Question 863163: a rectangular piece of cardboard has a length that is 3 inches longer than the width. A square 1.5 inches on a side is cut from each corner. the sides are then turned up to form an open box with a volume of 162 cubic inches. find the dimensions of the original piece of cardboard.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x for length
y for width
x=y+3
The square of side size 1.5 inches being removed before folding the flaps means that height will be 1.5 inches.

Cutting the specified corner piece makes these variable dimensions for the base:
(x-2(1.5)) and (y-2*1.5), meaning x-3 and y-3. Using substitution for x as described means that the dimensions are:
x-3=%28y%2B3%29-3=highlight_green%28y%29 for the LENGTH of the base!
and
highlight_green%28y-3%29 for the WIDTH of the base.

Formulate the volume equation.
y%28y-3%29%281.5%29=162
-
Simplify the volume equation.
y%5E2-3y=162%2F1.5
y%5E2-3y-108=0
Which is factorable:
%28y%2B9%29%28y-12%29=0
The sensible answer is highlight%28y=12%29 for the WIDTH.
Finding x, x=y+3, x=12%2B3=15, highlight%28x=15%29 for the LENGTH.