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AMC8 2027 - Self-practice Set 5 Question 14

AMC8 · AMC8 2027 - Self-practice Set 5

Question 14

Isosceles right triangles are constructed outward on the sides of a $3-4-5$ right triangle, as shown. Each capital letter represents the area of its triangle. Which statement is true?
Question illustration
  1. $X+Z=W+Y$
  2. $W+X=Z$
  3. $3X+4Y=5Z$
  4. $X+W=\frac12(Y+Z)$
  5. $X+Y=Z$