Question

PQRS is a quadrilateral in which PR and RS intersect at O show that PQ+QR+RS+SP>PR+QS

Answer 1

In a triangle, sum of two sides is more the third side.

So, in triangle PQR;

PQ + QR > PR                                     � (1)

In triangle PSR;

PS + SR > PR                                       � (2)

Adding (1) and (2);

PQ + QR + RS + SP > 2PR                                � (3)

Similarly, it can be proved that

PQ + QR + RS + SP > 2QS               � (4)

Adding (3) and (4);

2(PQ + QR + RS + SP) > 2(PR + QS)

i.e. PQ + QR + RS + SP > PR + QS

Hence, proved.