2023 · Q54
The corners of an equilateral triangular plate were cut in such a manner that it forms a regular hexagonal plate. What is the ratio of the area of the triangular plate to the area of the hexagonal plate?
Elementary MathematicsMensuration
- A2 : 1
- B3 : 2
- C4 : 3
- D5 : 3
Explanation
Cutting the corners of an equilateral triangle of side a to leave a regular hexagon removes three small corner triangles, leaving a hexagon of side a/3. The hexagon's area is 6 times the area of an equilateral triangle of side a/3: 6·(√3/4)(a/3)² = (2/3)·(√3/4)a². The original triangle has area (√3/4)a², so the ratio is 1/(2/3) = 3/2, i.e. 3:2. The answer is (B).