SOLUTION: A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2. length (larger dimension) width (sm

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2. length (larger dimension) width (sm      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 902467: A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2.
length (larger dimension)
width (smaller dimension)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
p = 200 ft, perimeter
A = 1875 ft^2, area
x and y are the unknown dimensions.

2x+2y=p and xy=A
-
2y=p-2x
y=p%2F2-x
Substitute into A equation.
x%28p%2F2-x%29=A
%28p%2F2%29x-x%5E2-A=0
-x%5E2%2B%28p%2F2%29x-A=0
highlight_green%28x%5E2-%28p%2F2%29x%2BA=0%29
You may find that substituting the values now allows you to factor the quadratic expression; but this is not always the case.
highlight%28x=%28%28p%2F2%29%2B-+sqrt%28%28p%2F2%29%5E2-4%2AA%29%29%2F2%29

You might try to examine the expression for any other simplifications; or you could substitute the values (if not done already) and use the result for x to evaluate y.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2.
length (larger dimension)
width (smaller dimension)


With length and width being L, and W, respectively, and perimeter being 200, we get:

2L + 2W = 200____2(L + W) = 2(100)_____L + W = 100_____W = 100- L ----- eq (i)

Since area = 1,875, then L(100 - L) = 1,875

100L+-+L%5E2+=+1875

L%5E2+-+100L+%2B+1875+=+0

Solve for L, the length of the garden. The negative value should be ignored. Then find W, or width. 

Then do a check!! 



If you need a complete and detailed solution, let me know!!



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/.