You are designing dinnerware. What is the length of a side of the smallest square plate on which a 20-cm chopstick can fit along a diagonal without any overhang?

Ahh -- another use for the Pythagorean theorem.

a^2 + b^2 = c^2

a^2 + a^2 = 20^2
2a^2 = 400
a^2 = 400/2
a^2 = 200
a = 14.142 cm

To find the length of a side of the smallest square plate on which a 20-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The theorem states that in a right 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 is the hypotenuse of a right triangle, and the sides of the triangle are the length of the square plate's side (which we need to find) and the overhang.

Let's denote the side length of the square plate as "x" and the overhang as "y". We can set up the equation as follows:

x^2 + y^2 = 20^2

Since we want to find the smallest square plate, the overhang should be zero, which means y = 0. Substituting this into the equation, we get:

x^2 + 0^2 = 20^2

Simplifying the equation further:

x^2 = 20^2
x^2 = 400

To solve for x, we can take the square root of both sides:

√(x^2) = √(400)
x = 20

Therefore, the length of a side of the smallest square plate on which a 20-cm chopstick can fit along the diagonal without any overhang is 20 cm.

;nlbkjbk

69 hehe