Question 56
A triangle with perimeter $P$ is divided into $k$ triangular pieces for some $k \ge 2$.
a. Show that there exists a piece with perimeter greater than $\frac{P}{k}$.
b. Show that if the initial triangle is equilateral, then there exists a piece with perimeter at least $\frac{P}{\sqrt{k}}$.
a. Show that there exists a piece with perimeter greater than $\frac{P}{k}$.
b. Show that if the initial triangle is equilateral, then there exists a piece with perimeter at least $\frac{P}{\sqrt{k}}$.