How do I get the area of these?A floor is to be padded by square tiles. Using this size of tile it will take 200 pieces to cover the floor but if 1 inch is taken away on each side of the tile it...

How do I get the area of these?

A floor is to be padded by square tiles. Using this size of tile it will take 200 pieces to cover the floor but if 1 inch is taken away on each side of the tile it will take 288 tiles to cover the same amount of area. What are the sizes of the tiles?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the area to be padded is x*y

Let the side of the tile be a.

==> The area of the tile is a^2

==> The area to be padded is 200*a^2

==> x*y = 200*a^2.............(1)

Now when after taking 1 inch from the sides, the sides now is (a-1) and the number of tiles are 288

==> Then the area is 288(a-1)^2

==> x*y= 288* (a-1)^2...................(2)

Now, from (1) and (2), we have:

==> 200a^2 = 288(a-1)^2

===> 200a^2 = 288 (a^2 -2a+1)

==> 200a^2 = 288a^2 -576a +288

==> 88a^2 - 576a +288 = 0

==>  11a^2 -72a +36 = 0

==> (11a -6)(a-6) = 0

==> a = 6/11 ( Not valid because we can not take one inch from the tile)

==> a= 6

Then, the size of the square tile is 6"x 6"

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