i) Radius of incircle = area/semi perimeter
= 504/72 = 7 cm
ii) If ABC is the triangle with C = 90 deg; O is the incenter; D, E & F are the contact points of the circle with sides, then
OD = OE = CD = CE = 7 cm.
So, BD = y - 7 = BF; AE = x - 7 = AF
[Tangents from same exterior point to the same circle are equal in measure]
{Refer sketch in -
https://www.bing.com/images/search?q=image+of+a+right+triangle+with+a+circle+inscribed+in+it&view=detailv2&&id=0246FF159F9CB9573B2F845239C332D98B48C647&selectedIndex=9&ccid=306yI8n8&simid=608032602731252068&thid=OIP.Mdf4eb223c9fc97349eec046f7979fef9o0&ajaxhist=0}
So perimeter = AF + AE + BD + BF + CD + CE
= 2x + 2y - 14 = 144
==> x + y = 79 ----- (1)
Area of triangle = (1/2)*x*y = 504
==> y = 1008/x ------ (2)
Substituting in (1) & simplifying,
x^2 - 79x + 1008 = 0
==> (x - 63)(x - 16) = 0
So x = 63 cm, being x > y