Question

what is the side length of the smallest Square plate on which a 38cm chopstick can fit along a diagonal without any overhang

Answer 1

To find the smallest square that can be drawn is

this is forming a right triangle with both of its sides same length

use the pythagorean theorem to find the measure of x

`\begin{gathered} a^2+b^2=c^2 \\ x^2+x^2=38^2 \\ 2x^2=1444 \\ x^2=(1444)/(2) \\ x^2=722 \end{gathered}`
`\begin{gathered} \text{take the square root to find the solution of x} \\ x=\sqrt[]{722} \end{gathered}`

decompose the number into primes

`\begin{gathered} x=\sqrt[]{2\cdot19\cdot19} \\ x=19\sqrt[]{2} \\ x=26.87\approx26.9 \end{gathered}`