2018 · Q99
In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A5 cm
- B12 cm
- C15 cm
- D10 cm
Explanation
Let XY = x; then AXY is equilateral with AX = AY = x, and by similarity XP = YQ = 30 - x. XY + XP + YQ = x + 2(30 - x) = 60 - x = 40 gives x = 20. Then BP = QC = 10, so PQ = 30 - 10 - 10 = 10 cm. Hence option D.