Question

A chessboard has an area of 324 square inches. There is a 1 - inch border around 64 squares on the board. What is the length of one side of the region containing a small squares?

Answer 1

Explanation:

the length of the whole board is 2 inches more than the length of the squares part (one inch all around)

(L + 2)^2 = 324 ___ L^2 + 4L + 4 = 324 ___ L^2 + 4L - 320 = 0

factoring ___ (L + 20)(L - 16) = 0

L + 20 = 0 ___ L = - 20 ___ negative value not realistic

L - 16 = 0 ___ L = 16

Answer 2

The length of one side of the region containing the small squares is 64 inches.

Let x be the length of one side of the region containing the small squares.

The area of the small squares is 64 * 1 = 64 square inches.

The area of the border is (x + 2)^2 - x^2 = 4x + 4 square inches.

Since the area of the small squares and the border is equal to the area of the chessboard, we have:

64 + 4x + 4 = 324

68 + 4x = 324

4x = 256

x = 64

Therefore, the length of one side of the region containing the small squares is 64 inches.