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1987 AMC 12 Question 21

AMC12 · 1987 AMC 12

Question 21

There are two natural ways to inscribe a square in a given isosceles right triangle. If it is done as in Figure $1$ below, then one finds that the area of the square is $441\text{ cm}^2.$ What is the area (in $\text{cm}^2$) of the square inscribed in the same $\triangle ABC$ as shown in Figure $2$ below?

Question illustration
  1. $378$
  2. $392$
  3. $400$
  4. $441$
  5. $484$