Question

(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.

Answer 1

9514 1404 393

Answer:

• n by n+1
• n = 47

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.

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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