A square chessboard is made up of 64 white and black squares arranged in 8 rows and 8 columns. The side length of each square is 2 inches. What is the perimeter of the chessboard?

Mathematics
A square chessboard is made up of 64 white and black squares arranged in 8 rows and 8 columns. The side length of each square is 2 inches. What is the perimeter of the chessboard?

ScanSolve AI Answer

Answer

29km\sqrt{29} km

Step 1: Dalton travels 5 km south and then 2 km west, forming a right triangle with legs of 5 km and 2 km.

Step 2: The straight-line distance dd from the starting point is the hypotenuse of the right triangle.

Formula:
d=(5 km)2+(2 km)2d = \sqrt{(5\ \rm km)^2 + (2\ \rm km)^2}

Step 3: Substitute the values.
d=25 km2+4 km2d = \sqrt{25\ \rm km^2 + 4\ \rm km^2}

Step 4: Simplify inside the square root.
d=29 km2d = \sqrt{29\ \rm km^2}

Step 5: Take the square root.
d=29 km5.39 kmd = \sqrt{29}\ \rm km \approx 5.39\ \rm km

Final answer: 29\sqrt{29} km
\sqrt{29 km}

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