There is a triangular park ABC in a colony The resident of Welfare Association colony wishes to divide - Maths - Triangles

Question

There is a triangular park ABC in a colony The resident of
Welfare
Association colony wishes to divide this park into two parts - one
for plantingtrees and raising a lawn and the other for providing
place for children to play Theydecided to divide the park by
creating a boundary along XY which is parallel to ACsuch that ar(
BXY) = 2ar(ACYX) State how this boundary XYcan be
drawn so that X and Y lie on AB and BC respectively??

Anuradha Sharma · Accepted Answer

The figure is shown above where area of triangle AXY

=
2×Area of quadrilateral AXYC

As XY ∥AC, In triangle BXY and BAC that are similar, Area of BXYArea of BAC=XYAC2Area of BXYArea of BXY+area of XYCA=XYAC2XYAC2=2x2x+x=2x3x=23So XYAC =23 =0
816or XY = 0
816 ACSo for making the arrangment mentioned in the question we have to choose XY such that it is 0
816 AC