Question 430114: Hi there!
I have a rectangle with an area of 1150 units. What is the height and width of this rectangle if the height and width are only whole numbers?
Please note that this rectangle is as close to a square as possible (the only reason it is not a perfect square is because the square root of 1150 is not a whole number)
I have tried to find the answer to this by taking the square root of 1150 and multiplying integers close to it together (e.g. 34*34, 34*34, 34*33, 35*33 etc) but still come up with nothing. If you could also show me a way to solve this kind of problem I would be very grateful, as I have a few other rectangle problems like this I need solving.
Thanks so much!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I have a rectangle with an area of 1150 units. What is the height and width of this rectangle if the height and width are only whole numbers?
Please note that this rectangle is as close to a square as possible (the only reason it is not a perfect square is because the square root of 1150 is not a whole number)
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The prime factored form of 1150 = 2*5^2*23
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The closest you can come to a square using whole numbers
is 23*2(25) = = 46*25
So one dimension is 46; the other is 25
The alternative answer would be 2*25 (23)
giving you dimensions 50 and 23.
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The 46*25 is closer to a square than 50*23
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Cheers,
Stan H.
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