SOLUTION: A square lawn is surrounded by a concrete walkway that is 2.0m wide, as shown in the diagram. If the area of the walkway equals the area of the lawn, what are the dimensions of the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A square lawn is surrounded by a concrete walkway that is 2.0m wide, as shown in the diagram. If the area of the walkway equals the area of the lawn, what are the dimensions of the      Log On


   

Question 390292: A square lawn is surrounded by a concrete walkway that is 2.0m wide, as shown in the diagram. If the area of the walkway equals the area of the lawn, what are the dimensions of the lawn? Round your answer to the nearest tenth of a meter.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
No figure is shown.
If the side of the lawn is x, and 2 is the width of the walkway:
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x%5E2+=+%28x%2B4%29%5E2+-+x%5E2
x%5E2+=+8x+%2B+16
x%5E2+-+8x+-+16+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-16+=+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=%28-8%29%5E2-4%2A1%2A-16=128.

Discriminant d=128 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+128+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+128+%29%29%2F2%5C1+=+9.65685424949238
x%5B2%5D+=+%28-%28-8%29-sqrt%28+128+%29%29%2F2%5C1+=+-1.65685424949238

Quadratic expression 1x%5E2%2B-8x%2B-16 can be factored:
1x%5E2%2B-8x%2B-16+=+%28x-9.65685424949238%29%2A%28x--1.65685424949238%29
Again, the answer is: 9.65685424949238, -1.65685424949238. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-16+%29

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x+=+4+%2B+sqrt%2832%29 Ignore the negative solution
x =~ 9.657 meters
x = 9.7 meters