SOLUTION: A rectangle has area of 600 square meters. its length and width are whole number which measurements give the smallest perimeter?
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Question 1119470: A rectangle has area of 600 square meters. its length and width are whole number which measurements give the smallest perimeter?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A rectangle has area of 600 square meters. its length and width are whole number which measurements give the smallest perimeter?
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It's the pair of integer factors closest to sqrt(600).
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The smallest perimeter for a rectangle with a given area is a square with sides equal to the square root of the area. So take the square root of the area. Round to the nearest integer. Check to see if this integer is a factor of the area. If it is, then this integer and the other factor of the area are the desired integer dimensions that yield the minimum perimeter. If not, you need to find the integer that is closest to the square root of the area and is also a factor of the area. For your problem, you are going to be done on the first try. Other values for the area could be a bit more challenging. Extra credit: What would the smaller dimension of a minimum perimeter rectangle be if the area were a prime number?
John
My calculator said it, I believe it, that settles it
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