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A courtyard has three walls with widths
measuring 27 feet, 18 feet, and 30 feet. The
builder plans to lay square tiles at the base of
each wall. The dimensions of the tiles must be
such that a whole number of them will exactly
fit the width of each wall. If all tiles must be the
same size what are the greatest dimensions
each tile can have?

Respuesta :

Using the greatest common factor, it is found that the greatest dimensions each tile can have is of 3 feet.

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  • The widths of the walls are of 27 feet, 18 feet and 30 feet.
  • The tiles must fit the width of each wall, thus, the greatest dimension they can have is the greatest common factor of 27, 18 and 30.

To find their greatest common factor, these numbers must be factored into prime factors simultaneously, that is, only being divided by numbers of which all three are divisible, thus:

27 - 18 - 30|3

9 - 6 - 10

No numbers by which all of 9, 6 and 10 are divisible, thus, gcf(27,18,30) = 3 and the greatest dimensions each tile can have is of 3 feet.

A similar problem is given at https://brainly.com/question/6032811

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