2025 · Q16
In a triangle ABC, AB + BC = 7.1 cm, BC + CA = 12.1 cm and CA + AB = 7.2 cm. What is the area of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A3 square cm
- B32 square cm
- C33 square cm
- D3.3 square cm
Explanation
Adding the three relations gives 2(AB+BC+CA) = 26.4, so the perimeter is 13.2 cm. Then AB = 13.2 − 12.1 = 1.1, BC = 13.2 − 7.2 = 6.0, CA = 13.2 − 7.1 = 6.1. Since 1.1² + 6.0² = 37.21 = 6.1², the triangle is right-angled with legs 1.1 and 6.0, and area = (1/2)(1.1)(6.0) = 3.3 cm², option (d).