We have four wooden triangles with sides $3, 4, 5$ centimeters. How many convex polygons can we make by all of these triangles? (Just draw the polygons without any proof) A convex polygon is a polygon which all of it's angles are less than $180^o$ and there isn't any hole in it. For example:
Problem
Source: IGO 2015 Elementary 1
Tags: geometry, convex, Elementary
gamerrk1004
13.09.2019 14:36
I was crossing across this IGO problem when I came up with a doubt ... Isn't there any mathematical way to solve such questions ?? (Please respond as quickly as possible ...)
NikoIsLife
15.09.2019 03:11
gamerrk1004 wrote: I was crossing across this IGO problem when I came up with a doubt ... Isn't there any mathematical way to solve such questions ?? (Please respond as quickly as possible ...) There isn't really a formula for finding the answer to this problem. There is a systematic way to list down all possible such polygons, however. One way to do this is by first labelling the four triangles as $A$, $B$, $C$ and $D$. Then, we first place triangle $A$. Next, "branch off" from this by drawing all possible ways to connect $B$ to $A$, and then, eliminate all the cases that are similar to each other. Next, draw all possible ways to connect $C$ to $B$, and so on, until you draw all possible ways for all four triangles.