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

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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)   (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
-


Substitute into A equation.




You may find that substituting the values now allows you to factor the quadratic expression; but this is not always the case.


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)   (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





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

Then do a check!! 



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