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a children's park is 350 m long and 200 m wide. It is surrounded by a pathway of uniform width. Suppose the total area of the park is 74464 m2. How wide is the pathway

Guest Jul 30, 2017
edited by Guest  Jul 30, 2017
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a children's park is 350 m long and 200 m wide. It is surrounded by a pathway of uniform width. Suppose the total area of the park is 74464 m2. How wide is the pathway

 

 

\((2x+350)(2x+200)=74462\\ 2(2x+350)(x+100)=74462\\ (2x+350)(x+100)=37231\\ 2x^2+200x+350x+35000=37231\\ 2x^2+550x-2231=0\\\)

 

2x^2+550x-2231=0 = {x=-(((sqrt(80087)+275)/2)), x=((sqrt(80087)-275)/2)}

x is approx 4m

 

The path is 4 metres wide. That is one generous path :)

Melody  Jul 30, 2017

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