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A chessboard is one large square made up of $8$ rows of $8$ equal sized smaller squares. Krysta has two chessboards. On one board, the small squares are $2$ inches by $2$ inches. On the other, they are $3$ inches by $3$ inches. How much longer is the diagonal of the larger board than the diagonal of the smaller board? If necessary, round your answer to the nearest tenth. $\newline$ ____ inches

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Pythagorean theorem

Full solution

Q. A chessboard is one large square made up of

8

rows of

8

equal sized smaller squares. Krysta has two chessboards. On one board, the small squares are

2

inches by

2

inches. On the other, they are

3

inches by

3

inches. How much longer is the diagonal of the larger board than the diagonal of the smaller board? If necessary, round your answer to the nearest tenth.

\newline

____ inches

Calculate side length: Calculate the side length of each chessboard. The smaller board has squares of $2$ inches, so the side length is $8 \times 2 = 16$ inches. The larger board has squares of $3$ inches, so the side length is $8 \times 3 = 24$ inches.
Use Pythagorean theorem: Use the Pythagorean theorem to find the diagonal of each board. For the smaller board, diagonal = $\sqrt{16^2 + 16^2} = \sqrt{256 + 256} = \sqrt{512} = 22.6$ inches.
Calculate diagonal: Calculate the diagonal for the larger board. Diagonal = $\sqrt{24^2 + 24^2} = \sqrt{576 + 576} = \sqrt{1152} = 33.9$ inches.
Find difference: Find the difference in the diagonals of the two boards. Difference = $33.9$ inches - $22.6$ inches = $11.3$ inches.

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