SOLUTION: Hi,i'm using factoring to solve problems,and I can't figure this out. Here's the question: A rectangular garden 30 meters by 40 meters has two paths of equal width crossing through

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi,i'm using factoring to solve problems,and I can't figure this out. Here's the question: A rectangular garden 30 meters by 40 meters has two paths of equal width crossing through      Log On


   

Question 29162: Hi,i'm using factoring to solve problems,and I can't figure this out. Here's the question: A rectangular garden 30 meters by 40 meters has two paths of equal width crossing through it.Find the width of each path if the total area covered by the paths is 325m^2.Thanks a lot!

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the paths be x meters.
The combined area of the two paths can be written:
40x+%2B+30x+-+x%5E2+=+325 The subtraction ofx%5E2 takes into account the overlapping area of the paths' intersection which would otherwise be counted twice. So now you need to solve the quadratic equation:
x%5E2+-70x+%2B+325+=+0 Factor.
%28x-65%29%28x-5%29+=+0 Apply the zero products principle.
%28x-65%29+=+0 and/or %28x-5%29+=+0
If x-65+=+0 then x+=+65 Discard this solution as the path can't be wider than the garden.
If x-5+=+0 then x+=+5 This solution is valid.
The width of the path is 5 meters.