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Question

The fireplace in a den measures 36 inches by 24 inches. It is surrounded by square tiles. Each tile has a side length of x inches. Write a completely simplified expression for the perimeter of the tile surround, and for the area of the tile.

Answer 1

The number of tiles could be 36 on each horizontal side and 24 on each vertical side which equals:

72 horizontal and 48 vertical tiles = 120 total tiles if they were 1" tiles, except to close in the 4 corners requires 4 more tiles so the total number of tiles is 124.

For easy numbers, lets assume each tile has an edge that is divisible into 24 and 72 evenly.

So each tile could be 24" 12", 8", 6", 4", or 2" square. Let x be the side of a square border tile.

Then the total number of tiles around the Perimeter would be 2(24/x + 72/x) + 4. The 2 represents the top and bottom rows and the left and right columns and the 4 being the 4 corner tiles.

The Area of the border would x²(24/x + 72/x) + 4x², with the 4x² being the 4 corners.