Question

In any quadrilateral, the sum of the lengths of four sides is greater than the two diagonals. Prove.​

Answer 1

Answer:

Let PQRS be the given quadrilateral.

In ∆PQR,

PQ + QR > PR ...(1)(Sum of any to sides of a triangle is greater than third side)

In ∆RSP,

RS + SP > PR ...(2)

In ∆PQS,

PQ + SP > QS ...(3)

In ∆QRS,

QR + RS > QS ...(4)

By adding (1), (2), (3) and (4),

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

=> PQ + QR + RS + SP > PR + QS

Hence, proved.

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