Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, R = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.

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Solution

Steps of Construction :

(i) Draw a line segment PQ = 5.4 cm.

(ii) With centre P and radius 4 cm. and with centre Q and radius 4.6 cm., draw arcs intersecting each other at R.

(iii) Join PR and QR.

(iv) Again with centre P and radius 3.5 cm. and with centre R and radius 4.3 cm. draw arcs intersecting each other at S.

(v) Join PS and RS.

PQRS is the required quadrilateral.

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In Fig. PQRS is a quadrilateral in which diagonals PR and QS intersect in O. [4 MARKS]

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

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and diagonals

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(Round-off to the nearest integer)

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