Question

If PQRS is a quadrilateral, then show that:
PQ+ QR + RS + PS > 2 (PR + QS)

Please answer it fastest as possible.....
it's my exam now​

Answer 1

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I PQRS is a quadrilateral in which diagonal PR and QS intersect at a O .

to prove - PQ +QR +RS+SP < 2 ( PR + QS )

proof -

we know that sum of any two side of a triangle is greater than the third side .

.'. in Δ PQO ,

PO+QO>PQ , .......................(i)

in Δ SOP

SO + PO >PS , .........................(ii)

in Δ SOR

SO + OR > RS ...........................(iii)

in Δ QOR ,

QO + OR > QR ...........................(iv)

on adding eqn. i , ii , iii & iv

we get ,

PO+QO+SO+PO+SO+OR+QO+OR > PQ+PS+SR+QR

also ⇒ 2 ( PO + QO + SO + OR ) > PQ+PS+SR + QR

= 2( PR + QS ) > PQ+PS+RS + QR ( proved) ....

Answer 2

∣Answer∣

I PQRS is a quadrilateral in which diagonal PR and QS intersect at a O .

to prove - PQ +QR +RS+SP < 2 ( PR + QS )

proof -

we know that sum of any two side of a triangle is greater than the third side .

.'. in Δ PQO ,

PO+QO>PQ , .......................(i)

in Δ SOP

SO + PO >PS , .........................(ii)

in Δ SOR

SO + OR > RS ...........................(iii)

in Δ QOR ,

QO + OR > QR ...........................(iv)

on adding eqn. i , ii , iii & iv

we get ,

PO+QO+SO+PO+SO+OR+QO+OR > PQ+PS+SR+QR

also ⇒ 2 ( PO + QO + SO + OR ) > PQ+PS+SR + QR

= 2( PR + QS ) > PQ+PS+RS + QR ( proved) ....

Step-by-step explanation:

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