Geometry

inradius ,  r   for  a right triangle  =

[  sum  of two  leg  lengths  -  hypotenuse  ]    /   2

The  sum of  the two  leg lengths =   1276  -  533  =  743

So

r  =    [ 743  - 533  ]  /  2    =     210  / 2  =  105

A right-angled triangle has a perimeter of 1276 and the longest side of 533.  What is the length of the inradius?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

P = 1276          s = 1276 / 2           Hypotenuse c = 533

Short leg = a         long leg = b            a + b = 743

a² + (743 - a)² = c²

a = 308           b = 435

A = 1/2(ab)

Inradius     r = A / s = 105