Question

If PS is a median of triangle PQR and T is any point on PR such that ar(PST):ar( PQS) = 2:3, then ar(TSR): ar (PQR)

Answer 1

•PS is a median of triangle PQR and T is any point on PR such that ar(PST):ar( PQS) = 2:3

•Let ar(PST) = 2x and ar(PQS) = 3x

•Since PS is the median of ΔPQR,

ar(PQS) = ar(PSR) = ar(PST) + ar (TSR)

implies, 3x = 2x + ar(TSR)

implies, ar(TSR) = x

•Now, ar(PQR) = ar(PQS) + ar(PST) + ar(TSR) = 3x + 2x + x = 6x

•Therefore, ar(TSR) : ar(PQR) = 1:6