SOLUTION: a rectangular lawn has an area of 667 square meters. Surrounding the lawn is a flower border 4 meters wide. The border alone has an area of 548 square meters. A circular sprinkle

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Question 871475: a rectangular lawn has an area of 667 square meters. Surrounding the lawn is a flower border 4 meters wide. The border alone has an area of 548 square meters.
A circular sprinkler is installed in the middle of the lawn. What is the spraying radius of the sprinkler if it covers the entire yard, including the flower border?
Explain, in detail, all the reasoning, algebra, and problem-solving techniques you use to solve this problem. Represent all variables and include key steps and formulas you used. thank you for your help,
Harry

Answer by josgarithmetic(39838) (Show Source):
You can put this solution on YOUR website!
Dimensions x and y.
A diagonal is the size of the diameter of the sprinkler reach.

Lawn is xy=667.
Flower border AND lawn is (x+2*4)(y+2*4)=(x+8)(y+8).
Just the flower border is (x+8)(y+8)-xy=548, the value been given.

Simplify the border equation.

Now we have a system of two equations in x and y.
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xy=667
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2x+2y=137
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substititute.

Check discriminant, 137^2-4*2*1334=18769-10672=8097

x=56.746 or x =11.754;
resulting y,
y=11.754 or y=56.746

Wanted was garden AND border, so staying with decimals, one dimension is 56.746+8 and other dimension is 11.754+8. Those are 64.748 and 19.754.
Diameter, same as the diagonal is ; and since question asks for the radius of this circular spray pattern area reached, the radius is:
.