Problem:
Right isosceles triangles are constructed on the sides of a right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?
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Answer Choices:
A.
B.
C.
D.
E.
Solution:
The areas are and . Therefore, is correct. . The other choices are incorrect.
By the Pythagorean Theorem, if squares are constructed on each side of any right triangle, the sum of the areas of the squares on the legs equal the area of the square on the hypotenuse. So , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions