Olympiad workbookIOQMProperties of Triangles

The sides x and y of a scalene triangle satisfy x+ 2 x =y+ 2 y , where is the area of the triangle. If x=60, y=63 , what is the length of the largest side of the triangle?

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aligned & 60+ 2 60 =63+ 2 63 & =1890 aligned Let third side be c and angle C aligned & 1 2 60 63 C=1890 & C=1 C= 2 aligned A B C is right triangle Longest side is hypotenuse =60^2+63^2 aligned & z^2=7569 & z=87 largest side. aligned

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