Julian takes a \(10\)-inch by \(10\)-inch square piece of paper and cuts it in half along the diagonal. He then takes one of the halves and cuts it in half again from the corner to the midpoint of the opposite side. All cuts are represented in the figure with dotted lines. What is the perimeter of one of the smallest triangles, in inches?

(A) \(10\)

(B) \(10\sqrt2\)

(C) \(20\)

(D) \(10+10\sqrt2\)

(E) \(10+20\sqrt2\)

Answer: D

Source: Manhattan GMAT