Tyler S.

asked • 09/10/12

Width of path surrounding pool

A pool measuring 14 meters by 26 meters is surrounded by a path of uniform width. If the area of the pool and path combined 988 square meters what is the width of the path. Equations for lenght of path 26+2x. Equation for width of path 14+2x. What is the width of the path in meters.

Simon B.

It is easier to solve the quadratic equation by first dividing both sides by 4 to get

x^2 + 20x - 156 = 0.

Then factor the left hand side to get

(x - 6)(x + 26) = 0. 

Now x = 6 or x = -26.  Since x = - 26 is not a possible path width, we have

x = 6.

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09/11/12

Bill M.

That is a very valid point.  The reason that I did not go that route is that not everyone is skilled at factoring quadratics and so I went with the guaranteed method of using the quadratic function   So, if that is the chosen method, then it is just as easy to solve the original equation.  But good observation.

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09/11/12

1 Expert Answer

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Bill M. answered • 09/10/12

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Area of pool and path = 988

Area is (14+2x)(26+2x) = 364 + 28x + 52x + 4x^2 = 988

So,

       4x^2 + 80x - 624 = 0

Using x = -b +- Sqrt(b^2 - 4.a.c)/2.a  we get x = -80 +- Sqrt(80^2 - 4.(4).(-624))/8

This gives two results x = 6 and x = -26 (x = -26 is extraneous)

Therefore x = 6

 

Now, width = 14 + 2(6) = 26

       Length = 26 + 2(6) = 38

Check 26x38 = 988 which is the combuined area.

 

So width of path is 6 meters.

 

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