Question

If s is any point on the side qr of triangle pqr prove that pq+qr+rp>2ps

Answer 1

In ΔPQS
Sum of any two sides is greater than the third side.
So, PQ + QS > PS ......(1)

In ΔPSR
Sum of any two sides is greater than the third side.
So, PR + SR > PS ...(2)

Adding equations (1) and (2)

PQ + PR + QS + SR > PS + PS

PQ + PR + QR > 2PS   [ QS + SR = QR]

Answer 2

In ΔPQS

Sum of any two sides is greater than the third side.

So, PQ + QS > PS ......(1)

In ΔPSR

Sum of any two sides is greater than the third side.

So, PR + SR > PS ...(2)

Adding equations (1) and (2)

PQ + PR + QS + SR > PS + PS

PQ + PR + QR > 2PS   [ QS + SR = QR]