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Question

The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?

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Solution


Let the given quadrilateral be ABCD in which diagonals AC is equal to 6 cm and BD is equal to 8 cm.Also, it is given that the diagonals bisect each other at right angle, at point O. AO=OC=12AC=3 cmAlso, OB=OD=12BD=4 cmIn right AOB:AB2=OA2+OB2AB2=(9+16) cm2AB2=25 cm2AB=5 cmThus, the length of each side of the quadrilateral is 5 cm.

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