In triangleRST,angle S is right angle.The mid points of two sides RS ans ST are X and Y respectively.Let us prove that, RY^2+XT^2=5XY^2?

1 Answer
Aug 14, 2017

see explanation

Explanation:

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Let #RX=XS=a, and SY=YT=b#, as shown in the figure.
#DeltaRSY, DeltaRST, DeltaXSY and DeltaXST# are right triangles.
By Pythagorean theorem, we get
#XY^2=a^2+b^2#
#RY^2=(2a)^2+b^2=4a^2+b^2#
#XT^2=a^2+(2b)^2=a^2+4b^2#
#=> RY^2+XT^2=4a^2+b^2+a^2+4b^2=5(a^2+b^2)=5XY^2#

Hence, #RY^2+XT^2=5XY^2# (proved).