You are here:

- Home
- Science
- Mathematics
- Advanced Math
- Lenght, Width - Solution / Explanation

Advertisement

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.

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 yd².

Therefore, the equation for the combined area is

(x+8)((15,200/x)+8) = 17,304

expand the equation

15200 + 8·15200/x + 8x + 8² = 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 + x² = 0

rearrange to standard form

x² - 255x + 15200 = 0

By the quadratic formula,

x = [255 ± √(255² – 4·1·15200)] / [2·1]

= [255 ± √4225] / 2

= [255 ± 65] /2

= 95, 160

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

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Friendly, prompt, courteous response !! |

Advanced Math

Answers by Expert:

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.**Publications**

Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language**Education/Credentials**

I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.**Past/Present Clients**

George White Elementary School.
Homework Help program at the Ridgewood Public Library, Ridgewood, NJ.
Individual students.