2019 · Q45
Let two lines p and q be parallel. Consider two points B and C on the line p and two points D and E on the line q. The line through B and E intersects the line through C and D at A in between the two lines p and q. If AC : AD = 4 : 9, then what is the ratio of the area of △ABC to that of △ADE?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2:3
- B4:9
- C16:81
- D1:2
Explanation
Triangles ABC and AED have vertical angles at A and alternate interior angles from p || q, so they are similar with linear ratio AC:AD = 4:9. Area ratio = 16:81.