Question 20
The measures of the smallest angles of three different right triangles sum to $90^\circ$. All three triangles have side lengths that are primitive Pythagorean triples. Two of them are $3$-$4$-$5$ and $5$-$12$-$13$. What is the perimeter of the third triangle?
(A) $40$
(B) $126$
(C) $154$
(D) $176$
(E) $208$
(A) $40$
(B) $126$
(C) $154$
(D) $176$
(E) $208$