Question

in triangle pqr angle q=90° pq is 12 and qr is 5 and qs is bisector of angle q and median of side pr find length of qs

Answer 1

when ce draw median of right angled triangle the centroid is on the mid point of hypotenuse. In triangle PQR the centroid is at S,which is the mid point of PR.

PR2 = PQ2 + QR2

     = 122 + 52 = 144 + 25 = 169

Therefore PR= 13

RS = PS = 13/2=6.5

Sis the centroid , RS =PS =QS=6.5

Answer 2

In the attachments I have answered this problem.

Concept:

1. In a right angled triangle, square

on the hypotenuse is equal to sum of the squares on the other two sides.

2. The midpoint of right angled triangle is equidistant from its vertices.

I hope this answer helps you