Answers

2016-03-27T16:08:17+05:30
Given: PQR is a triangle
           X divides the base QR in the ratio of 2:1 i.e., QX= 1/2 XR
rtp: 
ar triangle PQX =1/3ar triangle PQR
construction: join PX
                     draw an altitude PY for 
triangle PQR
proof: area of triangle PQX = 1/2 *PY*QX
           area of triangle PXR = 1/2 * PY * XR
                                            = 1/2 * PY * 2QX
                                            = 2(1/2 * PY * QX)
                                            = 2( area of triangle PQX)
we know that, area of triangle PQR = area of triangle PQX + area of                                                                   triangle PXR
                                                         = 
3( area of triangle PQX)
area of triangle PQX = 1/3(area of triangle PQR )
hence proved
2 4 2