2024 · Q85
In a triangle ABC, AB = 21 cm, BC = 20 cm and CA = 13 cm. A perpendicular CD is drawn upon the longest side. What is the area of the triangle BCD?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A96 square cm
- B84 square cm
- C80 square cm
- D72 square cm
Explanation
Heron: s = 27, area = √(27×6×7×14) = 126. Altitude to the longest side: CD = 2×126/21 = 12; AD = √(13²−12²) = 5, so DB = 16. Area of BCD = ½×16×12 = 96 sq cm — option A.