(c) There is a square tile pattern of n by n tiles and a row of n tiles. All the tiles are of the same size. If the row of n tiles is joined to the square pattern to form a rectangular pattern, what are the dimensions of the rectangle? (d) If there are 2,256 pieces of tiles in the rectangular pattern in (c), find the value of n.

9514 1404 393

Step-by-step explanation:

If the square starts as n rows of n columns, adding another row of n columns will make a rectangle with dimensions n+1 rows by n columns.

__

The total number of tiles in the rectangle is said to be ...

  n(n+1) = 2256

  n^2 +n +1/4 = 2256 1/4 . . . complete the square

  (n +1/2)^2 = (47 1/2)^2 . . . . rewrite as squares

  n = 47