Step 1: Draw a line segment BC of 8 cm.
Step 2: Draw angle B= 90 degrees.
Step 3: With B as centre and radius 13.5 cm, draw an arc which intersects BX at D.
Step 4: Join D to A.
Step 5: Draw the perpendicular bisectors of segment DA. It intersects the line segment BD at point C.
Step 6: Join C to A.

Thus, triangle ABC is the required triangle.