SOLUTION: hi, I was hoping you can help me on this: A rectangular lawn measures 8m by 6m. The owner wants to get a uniform border of trees along two adjacent sides of the lawn. If the tre

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: hi, I was hoping you can help me on this: A rectangular lawn measures 8m by 6m. The owner wants to get a uniform border of trees along two adjacent sides of the lawn. If the tre      Log On


   

Question 204658: hi, I was hoping you can help me on this:
A rectangular lawn measures 8m by 6m. The owner wants to get a uniform border of trees along two adjacent sides of the lawn. If the tress cover an area of 8m^2, how wide is the border?
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
If the border width is x, then the area is area+=+6x%2B8x%2Bx%5E2
Since area is 8m%5E2, you have x%5E2%2B14x=8
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B14x%2B-8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2814%29%5E2-4%2A1%2A-8=228.

Discriminant d=228 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+228+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+0.54983443527075
x%5B2%5D+=+%28-%2814%29-sqrt%28+228+%29%29%2F2%5C1+=+-14.5498344352707

Quadratic expression 1x%5E2%2B14x%2B-8 can be factored:
1x%5E2%2B14x%2B-8+=+1%28x-0.54983443527075%29%2A%28x--14.5498344352707%29
Again, the answer is: 0.54983443527075, -14.5498344352707. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B14%2Ax%2B-8+%29


You should discard the negative answer, as it is meaningless.