SOLUTION: thanks for your help. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^, what is the width of t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: thanks for your help. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^, what is the width of t      Log On


   

Question 28978: thanks for your help. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^, what is the width of the path?
A=(2)LW
2x30.20=1200
1200-400=800 sq ft left

could the path be 20 ft wide? 20 times 20 times 2=800
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It sounds like the path is constructed IN and not AROUND the garden, so
it diminishes the amount of gardent area.
Let the uniform width of the path be "x".
If you draw the picture you will see that the remaining garden space is
a rectangle with a width of 30-2x and a length of 20-2x.
EQUATION:
(30-2x)(20-2x)=400
2(15-x)2(10-x)=400
(15-x)(10-x)=100
150-25x+x^2=100
x^2-25x+50=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-25x%2B50+=+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=%28-25%29%5E2-4%2A1%2A50=425.

Discriminant d=425 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--25%2B-sqrt%28+425+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+425+%29%29%2F2%5C1+=+22.8077640640442
x%5B2%5D+=+%28-%28-25%29-sqrt%28+425+%29%29%2F2%5C1+=+2.19223593595585

Quadratic expression 1x%5E2%2B-25x%2B50 can be factored:
1x%5E2%2B-25x%2B50+=+1%28x-22.8077640640442%29%2A%28x-2.19223593595585%29
Again, the answer is: 22.8077640640442, 2.19223593595585. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-25%2Ax%2B50+%29

Hope this helps
Cheers,
Stan H.