Question

52) If PQRS is a quadrilateral and PR is one of its diagonals, then which of the following is always true ? (1) PQ + QR + RS + SP > 3PR (2) PQ + QR + RS + SP < 2PR (3) PQ + QR + RS + SP > 2PR (4) PQ + QR + RS + SP = 2PR

Answer 1

The answer is option 2 

Answer 2

Given,

PQRS is a quadrilateral.

To Find,

The relation between the sum of all four sides and the diagonal dimensions.

Solution,

In a quadrilateral, the sum of all four sides is always greater than two times the diagonal.

Option 2, which states PQ+QR+RS+SP < 2PR is false.

Similarly, option 4, stating PQ+QR+RS+SP = 2PR is false.

Option 1, stating PQ+QR+RS+SP > 3PR may not be true always.

Henceforth, option 3, stating PQ+QR+RS+SP > 2PR is always true in the case of a quadrilateral.