2026 · Q88
For the next two (02) items that follow : ABC is an equilateral triangle. BP is perpendicular to AC, PR is perpendicular to AB, and PQ is perpendicular to BC. What is the ratio of the area of ΔPRB to the area of ΔPQC?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 : 1
- B2 : 1
- C3 : 1
- D3 : 2
Explanation
Triangle PRB is right-angled at R with PR = s√3/4 and RB = √(PB² − PR²) = 3s/4, so its area is ½·(s√3/4)(3s/4) = 3√3s²/32. Triangle PQC has PC = s/2 with PQ = (s/2)sin 60° = s√3/4 and CQ = (s/2)cos 60° = s/4, so its area is ½·(s√3/4)(s/4) = √3s²/32. The ratio is 3 : 1, option C.