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smc

geometry senior

Problem

The base of a new rectangle equals the sum of the diagonal and the greater side of a given rectangle, while the altitude of the new rectangle equals the difference of the diagonal and the greater side of the given rectangle. The area of the new rectangle is:
(A)
(B)
(C)
(D)
Solution
Let the larger side of the rectangle be y and the smaller side of the rectangle be x. Then, by pythagorean theorem, the diagonal of the rectangle has length . By the definition of the problem, the area of the new rectangle is Expanding this gives the area of the new rectangle to be , or .
Final answer
C