If each small square on a grand chest board is 2 cm x 2 cm and the diagonal on the whole board measures square root of 800 cm. How many small squares are on the board?
each edge=800*.707=560cm
that is a really big chess board, bigger than my woodshop.
so 560/2=280 squares along one edge, so total squares=280*280
Geepers.
To determine the number of small squares on the chessboard, we need to calculate the total area of the board and then divide it by the area of each small square.
The diagonal of the chessboard forms a right-angled triangle with two adjacent sides measuring 2 cm (one side of a small square) and the hypotenuse measuring √800 cm. Using the Pythagorean theorem, we can solve for the missing side:
a^2 + b^2 = c^2
(2 cm)^2 + (2 cm)^2 = (√800 cm)^2
4 cm^2 + 4 cm^2 = 800 cm
8 cm^2 = 800 cm
Now we can find the length of one side of the chessboard by taking the square root of the area:
x^2 = 800 cm
x = √800 cm
x ≈ 28.284 cm (rounded to three decimal places)
The length of one side of the chessboard is approximately 28.284 cm. As each side of the chessboard is made up of small squares measuring 2 cm x 2 cm, we can find the number of small squares by dividing the total length of one side by the length of one small square:
28.284 cm ÷ 2 cm = 14.142
However, since we are looking for the number of small squares on the entire chessboard, we need to square the result:
14.142 x 14.142 = 200
Therefore, there are approximately 200 small squares on the chessboard.