A) No; 9.3 or 20.6.
B) Yes, because the triangles are similar.
C) No, because the triangles will not necessarily be similar.
There is not enough information to answer Questions 2 or 3.
Explanation for Question 1:
A) We are not told which side is the longest, so these two sides could be placed anywhere in the Pythagorean theorem. They could either be both legs, or one could be the hypotenuse:
Hypotenuse: 13² + b² = 16²
169 + b² = 256
169 + b² - 169 = 256 - 169
b² = 87
b = √87 = 9.3
Both legs: 13² + 16² = c²
169 + 256 = c²
425 = c²
√425 = c
20.6 = c
B) The two triangles will be similar, since each pair of corresponding sides will have the same ratio (2, since it is doubled). Similar triangles have the same angle measures, so this must also be a right triangle.
C) Simply adding a value to each side will not preserve similarity. For example, if we had a triangle with sides 3, 4, and 5, adding 2 to each side would give us 5, 6 and 11. These do not have the same ratios; 3/5 is not the same as 4/6 or 5/11.