SOLUTION: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width if the area of the pool and path combined is 416 square meters what is the width of the path

Algebra ->  Expressions -> SOLUTION: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width if the area of the pool and path combined is 416 square meters what is the width of the path      Log On


   

Question 895844: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width if the area of the pool and path combined is 416 square meters what is the width of the path
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Total dimensions: Using w for width of the path,
2w+10 and 2w+20.
%282w%2B10%29%282w%2B20%29=416 to account for combined pool area and path area.

Simplify.
2%28w%2B5%292%28w%2B10%29=2%2A2%2A104
%28w%2B5%29%28w%2B10%29=104
w%5E2%2B15w%2B50=104
w%5E2%2B15w-54=0
Discriminant, 15%5E2%2B4%2A54=441=21%5E2
w=%28-15%2B21%29%2F2
highlight%28w=3%29

That quadratic IS factorable as (w-3)(w+18) and the equation could be solved through factoring.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width if the area of the pool and path combined is 416 square meters what is the width of the path


Let UNIFORM width of path, be W

Then width on either end of pool = W + W, or 2W

Area of pool and path = (2W + 10)(2W + 20), and area of pool and path = 416.

Thus, (2W + 10)(2W + 20) = 416

4W%5E2+%2B+60W+%2B+200+=+416

4W%5E2+%2B+60W+%2B+200+-+416+=+0

4W%5E2+%2B+60W+-+216+=+0

4%28W%5E2+%2B+15W+-+54%29+=+4%280%29

W%5E2+%2B+15W+-+54+=+0

(W - 3)(W + 18) = 0 

W, or width of path = highlight_green%28highlight_green%283%29%29 m

You can do the check!! 



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL

MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,

GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.