SOLUTION: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth. A rectangular piece of cardboard is made into a box by cutting 3 inches

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth. A rectangular piece of cardboard is made into a box by cutting 3 inches       Log On


   

Question 1029169: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth.
A rectangular piece of cardboard is made into a box by cutting 3 inches squares from each corner and then folding the cardboard up. The length of the cardboard box is 3 inches more than its width. If the volume of the box is 540 inches^3, what are the dimensions of the original piece of cardboard?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                     Number                    Revision
Box height             3                         3
Base length            L-2*3                     L-6
Base width             w-2*3                     w-6
Length description     L-2*3=3+(w-2*3)          L-6=w-3

volume is 3%28L-6%29%28w-6%29=540

Use the description's relation between L and w to substitute for one of them.
L-6=w-3
L=w-3%2B6
L=w%2B3---------* You will use this again further down to finish.
-
3%28w%2B3-6%29%28w-6%29=540
3%28w-3%29%28w-6%29=540
%28w-3%29%28w-6%29=540%2F3
%28w-3%29%28w-6%29=9%2A2%2A10
%28w-3%29%28w-6%29=180
w%5E2-9w%2B18-180=0
w%5E2-9w-162=0

General solution formula for quadratic equation:
Discriminant, 81%2B4%2A162=729=27%5E2;
w=%289%2B27%29%2F2
highlight%28w=18%29

Find from that, highlight%28L=21%29