Please solve q 88?

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1 Answer
May 20, 2018

option (1) 144

Explanation:

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We know that the ratio of areas of two similar triangle is equal to the squares of the ratio of lengths of their corresponding sides.

Here #Delta ABC# is similar to #DeltaPQR,DeltaPST and DeltaPUV#

So #(DeltaPQR)/(Delta ABC)=(PR)^2/(AB)^2#

#=>9/(Delta ABC)=(AS)^2/(AB)^2#

#=>sqrt(9/(Delta ABC))=(AS)/(AB)#

#=>3/sqrt(Delta ABC)=(AS)/(AB).......[1]#

Similarly

#(DeltaPST)/(Delta ABC)=(ST)^2/(AB)^2#

#=>49/(Delta ABC)=(ST)^2/(AB)^2#

#=>sqrt(49/(Delta ABC))=(ST)/(AB)#

#=>7/sqrt(Delta ABC)=(ST)/(AB).......[2]#

And also

#(DeltaPUV)/(Delta ABC)=(PU)^2/(AB)^2#

#=>4/(Delta ABC)=(BT)^2/(AB)^2#

#=>sqrt(4/(Delta ABC))=(BT)/(AB)#

#=>2/sqrt(Delta ABC)=(BT)/(AB).......[3]#

Adding {1] ,[2] and [3] we get

#3/sqrt(Delta ABC)+7/sqrt(Delta ABC)+2/sqrt(Delta ABC)=(AS)/(AB)+(ST)/(AB)+(BT)/(AB)#

#=>12/sqrt(Delta ABC)=(AS+ST+BT)/(AB)=(AB)/(AB)=1#

#=>DeltaABC=12^2=144#