The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? Use the picture below to help you. (I put the image below)

Question

The dimensions of Eric’s pool are 9 feet by 7 feet.  He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? Use the picture below to help you. (I put the image below)

anonymous · Answer

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campbell_st · Answer

well I'll assume that the walkway is a uniform width. 

ao you are adding 2x to the length and 2x to to the width.

|dw:1365100923909:dw|

so the total area of pool and walkway is 

$$(9 + 2x)\times ( 7 + 2x) = 143$$

which is a quadratic equation 

$$4x^2 + 32x + 63 = 143$$

the equation can be rewritten as

$$4x^2 + 32x - 80 = 0$$

divide each term by 4 gives

$$x^2 + 8x - 20 = 0$$

so you have to solve this quadratic, which can be factorised. 

only use the positive solution, as length can't be negative. 

hope this helps