SOLUTION: Find x if shaded area of a rectangle is 90(the whole rectangle is shaded except for the 3 holes). By developing and solving by factoring quadratic equation. The rectangle width is

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Find x if shaded area of a rectangle is 90(the whole rectangle is shaded except for the 3 holes). By developing and solving by factoring quadratic equation. The rectangle width is       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 200644: Find x if shaded area of a rectangle is 90(the whole rectangle is shaded except for the 3 holes). By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1.
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
I don't have a diagram of this situation but we can muddle through without one.
First, the big rectangle has an area of:
A%5B1%5D+=+%282x-2%29%283x%29
A%5B1%5D+=+6x%5E2-6x now we'll subtract the area of the three (3%28x%2A%28x-1%29%29) rectangular holes whose total area is:
A%5B2%5D+=+3x%5E2-3x to get:
A%5B1%5D-A%5B2%5D+=+6x%5E2-6x-%283x%5E2-3x%29
A%5Bt%5D+=+3x%5E2-3x and this, the problem tells us is 90, so...
3x%5E2-3x+=+90 Subtract 90 from both sides.
3x%5E2-3x-90+=+0 Factor out a 3 to facilitate the calculation.
3%28x%5E2-x-30%29+=+0 which means that...
x%5E2-x-30+=+0 Factor this quadratic equation.
%28x%2B5%29%28x-6%29+=+0 so...
highlight%28x+=+-5%29 or highlight_green%28x+=+6%29 Discard the negative solution as the length, x, can only be positive.