Question

in ∆PQR, point S is the midpoint of the QR. if PQ=12, PR=16, PS=10 then find the length of QR​

Answer 1

Step-by-step explanation:

In △PQR,

M is the midpoint of side QR ........ given

∴ PM is the median of the triangle.

By Apollonius theorem,

PQ

2

+PR

2

=2PM

2

+2QM

2

11

2

+17

2

=2PM

2

+2(

2

1

QR)

2

121+289=2PM

2

+2(6)

2

410=2PM

2

+72

2PM

2

=338

PM

2

=169

∴PM=13 cm ........Taking sq. roots