SOLUTION: can you help me figure out how to solve this problem using the proper quadratic equation? Ric cuts half a rectangular lawn, 40m by 30m, by moving strips of equal width around th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: can you help me figure out how to solve this problem using the proper quadratic equation? Ric cuts half a rectangular lawn, 40m by 30m, by moving strips of equal width around th      Log On


   

Question 4751: can you help me figure out how to solve this problem using the proper quadratic equation?
Ric cuts half a rectangular lawn, 40m by 30m, by moving strips of equal width around the perimeter.Darin cuts the small rectangle left. How wide a strip does Ric cut so that they share the work equally?
Thank you
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a rectangle, 40x30. Draw another rectangle inside this one. Let the width of grass cut by Ric be x.

So, we know several things now: total area = 40x30 = 1200

Darin area is (40-2x)(30-2x) which multiplies out and simplifies to 4x%5E2-140x%2B1200. Now this has to be half the total area, so must equal 600.

4x%5E2-140x%2B1200+=+600 and simplifying gives x%5E2-35x%2B150+=+0. Now this is the equation we need to solve to find x. It factorises nicely into (x-30)(x-5) = 0, so x is either 30 or 5. Now x=30 is not a physically correct answer to your question, so x=5

Thinking about this, lets have a look at the smaller rectangle: (40-2x)(30-2x) becomes (40-10)(30-10) --> 30x20 which is 600, which half of 1200, so correct.

jon.