2024 · Q83
In a rectangle ABCD, AC is one of the diagonals. If AC + AB = 3AD and AC - AD = 4 units, then what is the area of the triangle?
Elementary MathematicsQuadrilaterals and Polygons
- A24 square unit
- B36 square unit
- C48 square unit
- D72 square unit
Explanation
Let AB = x, AD = y, AC = d: d+x = 3y and d−y = 4 give x = 2y−4, d = y+4. From d² = x²+y²: (y+4)² = (2y−4)²+y², so y = 6, x = 8, d = 10. The diagonal halves the rectangle: area = ½×8×6 = 24 sq units — option A. Note: this key is disputed — verify against the official UPSC key.