SOLUTION: A rectangular patio is being built against the side of a house using 60 congruent square tiles. Determine the arrangement of tiles that requires the least amount of edging. Justify

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Question 1087377: A rectangular patio is being built against the side of a house using 60 congruent square tiles. Determine the arrangement of tiles that requires the least amount of edging. Justify your answer, including a description of any constraints that affected your solution strategy. 

Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
The area of the patio will be 60 square units, since each tile is one square unit.
A = l*w = 60 [1]
We need to minimize the perimeter (edging) around the patio:
P = 2(l + w)
From [1], w = 60/l
Thus P = 2(l + 60/l)
P will be a minimum if dP/dl = 0
dP/dl = 2 - 120/l^2 = 0
l = sqrt(60)
Therefore w = sqrt(60)
Thus the perimeter is minimized if the tiles are arranged in a square
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The correct answer is 6*10 arranging or 10*6 arranging.


You need to find the minimum of 2(x+y), where x and y are positive integer numbers under the condition xy = 60.


To simplify your arguments, consider all possible factoring of 60 into the product of two integer x and y :

60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10


and calculate 2*(x+y) for each pair.


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