2016 · Q61
The sides of a triangle are √(a²+b²), √(c²+a²) and (b+c) where a, b, c are positive. What is the area of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A√(a² + b² + c²)/2
- B√(a²b² + b²c² + c²a²)/2
- Ca(b+c)/2
- D√(3(a²b² + b²c² + c²a²))/2
Explanation
Place the triangle's vertices at (−b,0), (c,0) and (0,a): the side lengths are then √(a²+b²), √(a²+c²) and b+c, exactly as given. Its area is (1/2)(base)(height) = (1/2)(b+c)(a) = a(b+c)/2 (option C).