QUESTIONS 9 AND 10 REQUIRE WRITTEN SOLUTIONS WHICH MAY INCLUDE PROOFS....

10. X is a point inside an equilateral triangleABC. Y is the foot of the perpendicular fromX to AC, Z is the footof the perpendicular fromX toAB, andW is the foot of the perpendicular fromX toBC.The ratio of the distances ofX from the three sides of the triangle is 1 : 2 : 4 as shown in the diagram.BWZ2 4X1YCAIf the area ofAZXY is 13 cm

2

, find the area ofABC. Justify your answer. [5 marks]InvestigationIfXY :XZ:XW =a:b:c, find the ratio of the areas ofAZXY andABC. [2 bonus marks]2