The diagonals of a quadrilateral are 5 cm and 12 cm long if the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral.
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Answer:
AC and BD are the diagonal of quadrilateral ABCD
AC = 5cm
BD= 12cm
Let them intersect at point O
As the diagonals are perpendicularly bisecting each other
AO = 1/2*5
=5/2
B0= 1/2*12
=6cm
angle AOB=90°
(AB)^2=(AO)^2+(BO)^2
=(5/2)^2+6^2
=25/4+36
= 25*1+36*4/4
=25+144/4
=169/4
AB=13/2. (taking square root)
AB= 6.5
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