what is the side length of the smallest square plane on which a 38-cm chopstick can fit along a diagonal without any overhang.
To determine the side length of the smallest square plane on which a 38-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem.
Let's assume the length of one side of the square is 'x' cm. According to the Pythagorean theorem, the diagonal length of the square can be calculated as follows:
Diagonal length = √(x² + x²) = √(2x²)
Since the length of the chopstick is 38 cm and it perfectly fits along the diagonal, we can equate the diagonal length to 38 cm:
√(2x²) = 38
To find 'x,' we need to isolate it. Squaring both sides of the equation gives:
2x² = 38²
Simplifying further:
2x² = 1444
Dividing both sides by 2:
x² = 1444/2
x² = 722
Taking the square root of both sides:
x = √722
Hence, the side length, 'x,' of the smallest square plane on which a 38-cm chopstick can fit along the diagonal without any overhang is approximately equal to √722 cm or approximately 26.90 cm.
To find the side length of the smallest square plane on which a chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angle triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the chopstick represents the hypotenuse of a right-angle triangle, and the sides of the triangle represent the length and width of the square plane.
Let's assume the side length of the square plane is 's' cm. The length of the chopstick will be the hypotenuse of a right-angle triangle with sides 's' cm.
According to the Pythagorean theorem, we can write the equation as:
s^2 + s^2 = (38 cm)^2
Simplifying this equation, we get:
2s^2 = 1444 cm^2
Dividing both sides by 2, we get:
s^2 = 722 cm^2
To find the value of 's', we take the square root of both sides:
s = √(722 cm^2)
Calculating the square root, we find:
s ≈ 26.87 cm
Therefore, the side length of the smallest square plane on which a 38-cm chopstick can fit along a diagonal without any overhang is approximately 26.87 cm.
x^2 + x^2 = 38^2
2x^2 = 1444
x = √722 = .....