Question

PQRS is a quadrilateral in which diagonals PR and QS intersect in O.

Find the correct relation between perimeter and diagonals of the quadrilateral.

• A. PQ + QR + RS + SP > (PR + QS)
• B. PQ + QR + RS + SP < (PR + QS)
• C. PQ + QR + RS + SP < 2 (PR + QS)
• D. PQ + QR + RS + SP = (PR + QS)

Answer 1

The correct option is C

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

In $△$OPQ, we have

OQ + OP $>$ PQ ...(i)

In $△$OQR, we have

OQ + OR $>$ QR ...(ii)

In $△$ORS, we have

OR + OS $>$ RS ....(iii)

In $△$OSP, we have

OS + OP $>$ SP ....(iv)

Adding (i), (ii), (iii) and (iv), we get

PQ + QR + RS + SP $<$ 2 (PR + QS)