Question

in triangle pqr ,base qr is divided at x such that qx=1/2xr.prove that ar triangle pqx =1/3ar triangle per

Answer 1

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