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If the diagonals of a quadrilateral are 15cm and 9cm, what is the perimeter of the...
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I suggest you to consider the a parallelogram your convex quadrilateral. This quadrilateral cannot be a rectangle because of different values of the lengths of diagonals.
The lengths of diagonals are: AC = 9 cm and BD = 15 cm.
If the vertices of parallelogram are ABCD and the midpoints are MNPQ, then the segment MN denotes the midline of triangle ABD and the segment PQ denotes the midline of triangle CBD.
You need to remember that the midline is one half that of the base, hence MN = PQ = `BD/2` = `15/2 ` = 7.5 cm.
The segment MQ and NP are midlines in triangles BAC and DAC, hence:
MQ=NP=`AC/2` =`9/2` =4.5 cm.
The perimeter of rectangle MQNP = 2(7.5 + 4.5) = 24 cm.
Hence, evaluating the perimeter of rectangle MNPQ yields `P_(MNPQ) = 24 cm` .
Posted by sciencesolve on January 9, 2012 at 6:03 PM (Answer #2)
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