a chessboard has diagonals of lengths
40 m. what is the length of each side of
the board, to the nearest length of a
centimeter? Explain t on reasoning.
let each side be x m
then x^2 + x^2 = 40^2
2x^2 = 1600
x^2 = 800
x = √800 = 28.28 m
Wow, a chessboard which is 28 metres long????
Are you sure it wasn't 28 cm?
To find the length of each side of the chessboard, we need to use the diagonal length and apply the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (sides of the chessboard).
Let's denote the length of each side of the chessboard as "x". Since a square has all sides equal, we can use "x" to represent both horizontal and vertical sides.
Now, applying the Pythagorean theorem:
x^2 + x^2 = 40^2
2x^2 = 1600
Divide both sides by 2:
x^2 = 800
To find the value of "x", we'll take the square root of both sides:
√(x^2) = √(800)
x ≈ 28.28
So, the length of each side of the chessboard, to the nearest centimeter, is approximately 28 centimeters.