2023 · Q70
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?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A18 cm
- B20 cm
- C22 cm
- D24 cm
Explanation
With the central triangle Q (perimeter 12) sharing each of its sides with one outer triangle, every interior edge is counted twice in the perimeter sum. Thus 16 + 12 + 4 + 12 = L + 2·12, giving L = 44 − 24 = 20 cm (B).