19. In figure, S and T trisect the side QR of a right triangle POR, pr

1.	19. In figure, S and T trisect the side QR of a right triangle POR, prove that:Q S T R
Answer» LetQS = aThusQT = 2aand QR = 3a In triangle PQRPR^2 = PQ^2 + QR^2PR^2 = PQ^2 + 3a^2PR^2 = PQ^2 + 9a^2 Eqn 1 In triangle PQTPT^2 = PQ^2 + 4a^2 Eqn 2 In Triangle PQSPS^2 = PQ^2 + a^2 Eqn 3 Thus3 PR^2 + 5 PS^2 = 3 PQ^2 + 27a^2 + 5 PQ^2 + 5a^2 = 8 [ PQ^2 + 4a^2 ] = 8 PT^2Hence proved

19. In figure, S and T trisect the side QR of a right triangle POR, prove that:Q S T R

Answer»

LetQS = aThusQT = 2aand QR = 3a

In triangle PQRPR^2 = PQ^2 + QR^2PR^2 = PQ^2 + 3a^2PR^2 = PQ^2 + 9a^2 Eqn 1

In triangle PQTPT^2 = PQ^2 + 4a^2 Eqn 2

In Triangle PQSPS^2 = PQ^2 + a^2 Eqn 3

Thus3 PR^2 + 5 PS^2 = 3 PQ^2 + 27a^2 + 5 PQ^2 + 5a^2 = 8 [ PQ^2 + 4a^2 ] = 8 PT^2Hence proved