Triangle ABC has a = 8.1 cm, b = 12.3 cm and area 15 cm². Find the largest possible perimeter of triangle ABC.

correct substitution into the formula for area of a triangle      (A1)

eg  15 = \(\frac{1}{2}\) × 8.1 × 12.3 × sin C

correct working for angle C    (A1)

eg  sin C = 0.301114, 17.5245…, 0.305860

recognizing that obtuse angle needed      (M1)

eg  162.475, 2.83573, cos C < 0

evidence of choosing the cosine rule      (M1)

eg  a² = b² + c² − 2bc cos(A)

correct substitution into cosine rule to find c     (A1)

eg  c² = (8.1)² + (12.3)² − 2(8.1)(12.3) cos C

c = 20.1720    (A1)

8.1 + 12.3 + 20.1720 = 40.5720

perimeter = 40.6    A1 N4

[7 marks]