2020 · Q76
The length and breadth of a rectangle are in the ratio 4 : 3. Then what is the ratio of the area of the triangle formed by the parts of the diagonals with a long side to the area of the triangle formed by the parts of diagonals with a short side?
Elementary MathematicsQuadrilaterals and Polygons
- A3 : 4
- B4 : 3
- C16 : 9
- D1 : 1
Explanation
The diagonals bisect each other, so each of the four triangles has area ½ × (d₁/2) × (d₂/2) × sinθ — all equal to one-quarter of the rectangle. Any two are in ratio 1 : 1. Hence the areas of any two of these triangles are in the ratio 1 : 1.