AB=AC=x (let) and AB+BC+CA=36 ⇒x+x+BC=36 ⇒BC=36−2x . . . (i) Since, AD is perpendicular to BC. ∴BC=2×√x2−(12)2 . . . (ii) From Eq. (i) and Eq. (ii), 2×√x2−144=36−2x ⇒√x2−144=
36−2x
2
=18−x Square both sides, Square both sides, x2−144=324+x2−36x ⇒36x=324+144=468 ⇒x=