2015 · Q87
The sides of a triangle are 25 cm, 39 cm and 56 cm. The perpendicular from the opposite vertex on the side of 56 cm is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10 cm
- B12 cm
- C15 cm
- D16 cm
Explanation
This is a Heron-plus-altitude problem. With sides 25, 39, 56, the semiperimeter is s = 60, and area = √(60 × 35 × 21 × 4) = √176400 = 420 cm². The altitude to the 56 cm side is 2 × Area/base = 840/56 = 15 cm. Option (b) 12 cm comes from arithmetic slips in the Heron computation. Hence option (c).