Question 55379: a garden plot has an area of 120 square meters. The measure of the length and width are whole numbers. The length and width of the garden were selected so that the least amount of fencing was required to enclose the garden. What are the dimensions of this garden.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a garden plot has an area of 120 square meters. The measure of the length and width are whole numbers. The length and width of the garden were selected so that the least amount of fencing was required to enclose the garden. What are the dimensions of this garden.
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In a rectangle, the most area that can be obtained from a given perimeter is in the shape of a square, the square root of 120 would give the dimension of the side of a little less than 11 meters, however, it requires integer measurements so the closest we can come to it would be a rectangle which is 10 by 12, a perimeter of 44 meters. Any other dimensions would have a larger perimeter, i.e an 8 by 15 rectangel would have a perimeter of 46 meters.
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an algebra equation:
L * W = 120
L = 120/W
:
Perimeter = 2L + 2W
Substitute: 2(120/W) + 2W
:
Let x = W, y = perimeter
y = 2(120/x) + 2x
y = 240/x + 2x
:
If you plot this, you will find the minimum integer value for y is 44 meters.
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