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Printsmc
geometry intermediate
Problem
A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is . What is the area of the large square? 
(A)
(B)
(C)
(D)
Solution
Let the length of the longer side be , and the length of the shorter side be . We are given that . However, note that is also the length of a side of the larger square. Thus the area of the larger square is .
Final answer
A