1952 AHSME Problem 46

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:

\begin{array}{l} \text{(A) greater than the area of the given rectangle} \quad\\ \text{(B) equal to the area of the given rectangle} \quad\\ \text{(C) equal to the area of a square with its side equal to the smaller side of the given rectangle} \quad\\ \text{(D) equal to the area of a square with its side equal to the greater side of the given rectangle} \quad\\ \text{(E) equal to the area of a rectangle whose dimensions are the diagonal and the shorter side of the given rectangle} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.