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?

Expert Answers
hala718 eNotes educator| Certified Educator

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"