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the given figure, PQRS is a quadrilateral with diagonals PR and QS.w that PQ+QR+RS+PS> PR+ Qs. |
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Answer» IPQRS is a quadrilateral in which diagonalPR and QS intersect at aO .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 ..'. inΔ PQO , PO+QO>PQ , .......................(i) inΔ SOP SO + PO >PS , .........................(ii) inΔ SOR SO + OR > RS ...........................(iii) inΔ 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+QRalso⇒ 2 ( PO + QO + SO + OR ) > PQ+PS+SR + QR = 2( PR + QS ) >PQ+PS+RS + QR ( proved) .... |
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