2026 · Q54
ABC is a triangle in which (AB + BC) exceeds CA by 10 cm, (BC + CA) exceeds AB by 8 cm and (CA + AB) exceeds BC by 72 cm. What is the area of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A196 cm²
- B180 cm²
- C172 cm²
- D160 cm²
Explanation
Adding the three excess equations gives 2(AB + BC + CA) − (AB + BC + CA)… i.e. the perimeter AB + BC + CA = 10 + 8 + 72 = 90. Then CA = (90 − 10)/2 = 40, AB = (90 − 8)/2 = 41, BC = (90 − 72)/2 = 9. Since 9² + 40² = 81 + 1600 = 1681 = 41², the triangle is right-angled with area 9·40/2 = 180 cm², option B.