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A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths 13, 19, 20, 25 and 31, not necessarily in that order. The area of the pentagon is

(A) 459 sq. units

(B) 600 sq. units 

(C) 680 sq. units 

(D) 745 sq. units

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Correct option (D) 745 sq. units

See Fig.

Since r2 + s2 = e2, e = 31 or e = 19 is not possible. Therefore, e equal to 13, 20 or 25.

The possibilities for triplet {r, s, e} are {5, 12, 13}, {12, 16, 20}, {15, 20, 25}, {7, 24, 25}.

Since 16, 15 and 24 do not appear among any of pair wise differences of 13, 19, 20, 25, 31, we have  a = 19, b = 25, c = 31, d = 20, e = 13.

Hence required area = 745 sq. units.

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