A ∆ with sides 3,6,8cm. Now, a man runs around ∆ in such way that he is always at distance of 1cm from sides of∆ then how much distance will he travel

Question

I don't know to proceed in this question , I am not getting what will be the man's path . How to think about that path ?

Answer 1

Hint: As he runs along each side of the triangle, the path will be parallel to the side, and exactly as long as that side. As he rounds each corner, the path will be a circular arc of radius $1$ connecting the straight components. There will be three such circular components, and they will fit together exactly to form a circle of radius $1$ (draw a picture).

Answer 2

Clearly the man will be running parallel to the triangle's sides. The only problem arises in how he turns the corners. Here, he must stay 1cm from the vertex, so he'll turn the corners in circular arcs.