The length of diagonals of a rhombus are 24cm and 32cm,find the length of the side of the rhombus.
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given length of diagonal d1=24cm
d2=32cm
TO FIND:side of the rhombus
let ABCD be a rhombus and AC & BD are its diagonals meeting at o
now In triangle AOB
ANGLE AOB=90°
SO BY PYTHAGORAS THEOREM
AO .AO + BO.BO=AB.AB
d1/2.d1/2+d2/2. d2/2=AB.AB
(AO=1/2AC and BO =1/2BD SINCE DIAGONALS ARE PERPENDICULAR BISECTORS)
so 24/2.24/2+32/2.32/2=AB.AB
12.12+16.16=AB.AB
144+256=AB.AB
400=AB.AB
SO AB=20
d2=32cm
TO FIND:side of the rhombus
let ABCD be a rhombus and AC & BD are its diagonals meeting at o
now In triangle AOB
ANGLE AOB=90°
SO BY PYTHAGORAS THEOREM
AO .AO + BO.BO=AB.AB
d1/2.d1/2+d2/2. d2/2=AB.AB
(AO=1/2AC and BO =1/2BD SINCE DIAGONALS ARE PERPENDICULAR BISECTORS)
so 24/2.24/2+32/2.32/2=AB.AB
12.12+16.16=AB.AB
144+256=AB.AB
400=AB.AB
SO AB=20
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