SOLUTION: The area of a rectangular tennis court is 140 m2. Its length is 6 m shorter than twice its width. Find the length and width of the tennis court.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The area of a rectangular tennis court is 140 m2. Its length is 6 m shorter than twice its width. Find the length and width of the tennis court.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 954787: The area of a rectangular tennis court is 140 m2. Its length is 6 m shorter than twice its width. Find the length and width of the tennis court.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A=Area=140sqm; W=width; L=length=2W-6m
A=LW Substitute for W.
A=%282W-6%29%28W%29
140m%5E2=2W%5E2-6W Subtract 140m^2 from each side.
0=2W%5E2-6W-140m%5E2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 2W%5E2%2B-6W%2B-140+=+0) has the following solutons:

W%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=%28-6%29%5E2-4%2A2%2A-140=1156.

Discriminant d=1156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+1156+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+1156+%29%29%2F2%5C2+=+10
W%5B2%5D+=+%28-%28-6%29-sqrt%28+1156+%29%29%2F2%5C2+=+-7

Quadratic expression 2W%5E2%2B-6W%2B-140 can be factored:
2W%5E2%2B-6W%2B-140+=+2%28W-10%29%2A%28W--7%29
Again, the answer is: 10, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B-140+%29

W=10m ANSWER 1: The width is 10 meters.
L=2W-6m=2(10m)-6m=20m-6m=14m ANSWER 2: The length is 14 meters.
CHECK:
A=LW
140 sq m=(14m)(10m)
140 sq m=140 sq m