I firstly like this way a little bit more because I remember that p is the perimeter this is useful because obviously now if someone gives you inradius and a perimeter you can figure out the area of a triangle or someone gives you the area of the triangle and the perimeter you can get the inradius of it if given any two of these variables you can always get the third so for example if someone if this was a triangle right over here which is the most famous of the right triangles if I have a triangle that has length 3 4 and 5 we know this is a right triangle you can verify this from the pythagorean theorem and someone says what is the inradius of this triangle right over here well we can figure out the area pretty easily we know that this is a right triangle 3 squared plus 4 squared is equal to 5 squared so the area is going to be equal to 3 times 4 times one half so 3 times 4 times one half is 6 and the perimeter here is going to be equal to 3 plus 4 which is 7 plus 5 is 12 and so we have the area so let's write this the area is equal to one half times the inradius times the perimeter so here we have 12 is equal to one half times the inradius times the perimeter so we have oh sorry we have 6 let me write this the area 6 6 is equal to one half times the inradius times 12 and so in this situation one half times 12 is 6 6 is equal to 6r divide both sides by 6 you get r is equal to 1 so if you want to draw the inradius for this one which is kind of a neat result so let me draw some angle bisectors here this 3-4-5 right triangle has inradius of 1 so this distance equals this distance which is equal to this distance which is equal to 1 just kind of a neat result