Please solve q 95 ?

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1 Answer
May 12, 2018

The length of the longest side is #21#.

Explanation:

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In a #DeltaABC#,

#rarrcosA=(b^2+c^2-a^2)/(2bc)#

#rarrArea=(1/2)a*bsinC#

Now, #Area# of #DeltaABD=(1/2)*9*8*sinx=36sinx#

#Area# of #DeltaADC=(1/2)*8*18*sinx=72sinx#

#Area# of #DeltaABC=(1/2)*9*18*sin2x=81sin2x#

#rarrDeltaABC=DeltaABD+DeltaADC#

#rarr81sin2x=36*sinx+72*sinx=108*sinx#

#rarr81*2cancel(sinx)*cosx=108*cancel(sinx)#

#rarrcosx=(108)/162=2/3#

Applying cosine law in #DeltaABC#, we get,

#rarrcos2x=(9^2+18^2-a^2)/(2*9*18)#

#rarr2cos^2x-1=(405-a^2)/324#

#rarr2*(2/3)^2-1=(405-a^2)/324#

#rarr2*(4/9)-1=(405-a^2)/324#

#rarr-36=405-a^2#

#rarra^2=405+36=441#

#rarra=21#

Also, note that

#rarrsin2x=2sinxcosx#

#rarrcos2x=2cos^2x-1#