number theory geometry/math homework

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An artist wants to construct a rectangular wall from square tiles. the wall is 72 inches long & 42 inches wide. All sqare tiles must be the same size & length of the sides of the tiles must be a whole # . Find 3 different square tiles that could be used to completely fill the rectangular space with no tile overlapping the border. Determine the smallest # of square tiles that could be used to fill the rectangualr space.

Jul 6th, 2015

Thank you for the opportunity to help you with your question!

Given tiles are square.

Wall length=72 inch

Wall width=42 inch

72 is divisible by: 2,3,4,6,8,9,12,18,24,36

42 is divisible by: 2,3,6,7,14,21

Common of above mentioned numbers = 2,3,6 Ans (Required three tiles to completely fill the space on wall)


B) Largest tile = 6 x 6 ( that satisfies above criteria)

For width = 42/6 =7

For length=72/6=12

Area of total tiles= 84.  Ans

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 6th, 2015

Hi Sunny,

I am confused. the problems states to find three different sizes of square tiles that could be used to completely fill the rectangular space, with no tiles overlapping the border. Determine the smallest number of suare tiles that could be used to fill the rectangular space. I am assuming the the 3 different sizes should be used separately & not together.  Thank you so much for your help



Jul 9th, 2015

Yes, so what is problem?

Jul 9th, 2015

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Jul 6th, 2015
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