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PIMSO 2021 - Mathematics - Grade 10 - National Round Question 17

PIMSO Maths · PIMSO 2021 - Mathematics - Grade 10 - National Round

Question 17

The perimeter of a triangle formed by points A(1,2), B(3,-4), and C(-2,-3) is in the form $x\sqrt{2y}+\sqrt{2z}+\sqrt{2s}$. If y<s<z, what is the value of x+y+z-s?

Use the usual simplified-radical representation with positive integer coefficients and squarefree radicands.