106-2 triangle ABC is similar to triangle pqr, PM is median of TRIANGLE PQR lIf ar triangle abc = 289 - Maths - Triangles

Question

106-2 triangle ABC is similar to triangle pqr, PM is median of
TRIANGLE PQR lIf ar triangle abc = 289 cm2, BC=17 DEGREE mr=6
5cm,then the area of triangle pqm is

Manbar Singh · Accepted Answer

We have,∆ABC~∆PQR   givenar∆ABC = 289 cm2BC = 17 cmNow, MR = 6
5 cmSince PM is median to side PR of ∆PQR, so     QR = 2 MR⇒QR = 2×6
5 = 13 cmWe know that ratio of areas of 2 similar ∆'s is equal to squares of the ratio of their corresponding sides
   ar∆ABCar∆PQR = BCQR2⇒289ar∆PQR = 17132⇒ar∆PQR = 169 cm2We know that median of a ∆ divides it into 2 ∆'s of equal areas
So, ar∆PQM = 12ar∆PQR = 12×169 = 84
5 cm2

106-2 triangle ABC is similar to triangle pqr, PM is median of TRIANGLE PQR.lIf ar triangle abc = 289 cm2, BC=17 DEGREE mr=6.5cm,then the area of triangle pqm is