Please solve q 95 ?

![enter image source here]![enter image source here] (useruploads.socratic.orguseruploads.socratic.org)

1 Answer
May 12, 2018

The length of the longest side is 21.

Explanation:

enter image source here

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