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2002 AMC 8 Question 16

AMC8 · 2002 AMC 8

Question 16

Right isosceles triangles are constructed on the sides of a $3-4-5$ right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?

Question illustration
  1. $X + Z = W + Y$
  2. $W + X = Z$
  3. $3X + 4Y = 5Z$
  4. $X + W = \dfrac{1}{2}(Y + Z)$
  5. $X + Y = Z$