A triangle ABC has been divided into four smaller triangles P, Q, R, S whose perimeters are 16 cm, 12 cm, 4 cm and 12 cm respectively. P, R and S contain the vertices A, B and C respectively. What is the perimeter of the triangle ABC ? 

Formula used:

The perimeter of the triangle = Sum of three sides

Calculation:

Required perimeter = Perimeter of (P + R + S) - Perimeter of Q

Required perimeter = (16 + 4 + 12) - 12 = 20 cm.

Alternate MethodGiven:

Perimeter of triangle P = 16 cm

Perimeter of triangle R = 4 cm

Perimeter of triangle S = 12 cm

Perimeter of triangle Q = 12 cm

Corrected calculation based on your instructions:

Required perimeter = (Perimeter of P + Perimeter of R + Perimeter of S) - Perimeter of Q

So, Required perimeter = (16 cm + 4 cm + 12 cm) - 12 cm = 32 cm - 12 cm = 20 cm.

Therefore, the perimeter of the triangle ABC is indeed 20 cm. 

Additional Information

To find the perimeter of triangle ABC, we simply add the perimeters of triangles P, R, and S, and then we subtract the perimeter of triangle Q. This is because the sides of triangles P, R, and S form the outside of triangle ABC, but Q is inside and doesn't add to the outside length.

So, we calculate it like this: Add the perimeters of P (16 cm), R (4 cm), and S (12 cm) to get 32 cm. Then, we subtract the perimeter of Q (12 cm) because it's on the inside.

The final perimeter of triangle ABC is 20 cm (32 cm - 12 cm = 20 cm). This gives us the total length around triangle ABC.