The Problem 

Find the number of integer-sided isosceles obtuse-angled triangles with perimeter 2008.

  • Cosine Rule: If ABC is any triangle, \( \angle BAC  = \theta \) then \( AB^2 + AC^2 – 2\times AB \times AC \times \cos \theta = BC^2 \) .
  • Pythagoras Theorem: If ABC is a right angled triangle with \( \angle BAC  = 90^o\) then \( AB^2 + AC^2  = BC^2 \)
  • Triangular Inequality: Sum of two sides of a triangle is greater than the third side.

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