Question

XYZ is an equilateral triangle of side a units. O is a point inside triangle XYZ such that points A,B and C are mid points of XO,YO and ZO respectively. Find Ratio of ar(XYZ) and ar (ABC)

Answer 1

In △OCB and △OZYOC = 1/2 OZOB= 1/2 OBSo , △OCB ~△OZY We know In two similar triangles, the ratio of their areas is thesquare of the ratio of their sides. Ar(OBA)/Ar(OXY) = (OB/OZ)2= 1/4 or 4Ar(OBA)=Ar(OXY)and Ar(OCA)/Ar(OZX) = (OA/OZ)2= 1/4  or 4Ar(OCA)=Ar(OZX) Now adding all the three equations , we get 4 Ar(ABC) = Ar(XYZ) or ,Ar(XYZ) /Ar(ABC) = 1/4 

Answer 2

Answer:

equilateral side of triangle