SOLUTION: The Length of a rectangular label is three times its width. If the length is decreased by 1 while the width stayed the same, the area of the new label would be 44 square centimeter

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The Length of a rectangular label is three times its width. If the length is decreased by 1 while the width stayed the same, the area of the new label would be 44 square centimeter      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 107112This question is from textbook Beginning Algebra
: The Length of a rectangular label is three times its width. If the length is decreased by 1 while the width stayed the same, the area of the new label would be 44 square centimeters. Find the original length and the width of the label. This question is from textbook Beginning Algebra

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let W=width of label
Then Length(L)=3W
Length decreased by DISABLED_event_one= 3W-1
Area(A)=L*W
In this problem, W=W and L=(3W-1), So:
A=W(3W-1)=44 get rid of parens (distributive law)
3W^2-W=44 subtract 44 from both sides
3W^2-W-44=44-44 collect like terms
3W%5E2-W-44=0 quadratic in standard form and it can be factored:
(Note: How did I know that it could be factored??? First, I calculated
sqrt%28b%5E2-4a%2Ac%29and found it to be sqrt%28529%29 or 23 which tells me that it can probably be factored. Next, I commenced evaluating the possible factors (a total of eight possibilities) until I found the one that worked.)
%283W%2B11%29%28W-4%29=0, so:
3W%2B11=0
3W=-11----------------------disregard negative value for width
and:
w-4=0
W=4cm------------------width
3W=3%2A4=12 cm--------------------------original length
CK
4*(12-1)=44
4*11=44
44=44

Hope this helps----ptaylor