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Question
A rectangular park is enclosed a walkway 4 yards wide.  

Park- 15200 square yards.

Walkway- 2104 square yards.


Determine length and width of park.


Let x = length of park.

15200 / x = width.

(x + 4)(15200 / x + 8) = (15200 + 2104)= 17304 **

8x + 121600 / x + 15264 = 17304 **

8x^2 - 2040x = 121600 **

x^2 - 255x = 15200

x = 127 * 5 + - 32 * 5 = 160 or 95

length of park = 160 yards or 95 yards.

width of park = 15200 / 160 = 95 or 15200 / 95 = 160

** I don't understand these steps.

Also, can you provide some hints/tips on quadratics?  I am not very good at these.  Thanks.

Answer
Park and walkway
Park and walkway  
There is an error in the solution.
The length of the park is x.
The width of the park is 15200/x.

Since the walkway is 4 yd wide, it adds a total of 8 yds to both length and width. https://www.flickr.com/photos/dwread/15884823021/

Combined, the area of the park plus walkway is 15200+2104 = 17304 yd.
Therefore, the equation for the combined area is
(x+8)((15,200/x)+8) = 17,304

expand the equation
15200 + 815200/x + 8x + 8 = 17304

factor 8 out of each term
1900 + 15200/x + x + 8 = 2163
-255 + 15200/x + x = 0

multiply both sides by x
-255x + 15200 + x = 0

rearrange to standard form
x - 255x + 15200 = 0

By the quadratic formula,
x= [255 √(255 4115200)] / [21]
   = [255 √4225] / 2
   = [255 65] /2
   = 95, 160

The dimensions of the park are 95 yards by 160 yards.

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