Some Pythagoras triplets to cram

In any given exam there are about 2 to 3 questions based on Pythagoras theorem.  Wouldn't it be nice that you remember some of the Pythagoras triplets thus saving up to 30 seconds in each question. This saved time may be used to attempt other questions. Remember one more right question may make a lot of difference in UR PERCENTILE score.The unique set of Pythagoras triplets with the Hypotenuse less than 100 or one of the side less than 20  are as follows :

(3,4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97)….even more…
(15,112,113),   (17,144,145),   (19,180,181),   (20,99,101)

If you multiply the digits of the above mentioned sets by any constant you will again get a Pythagoras triplet .
Example : Take the set (3,4,5).
Multiply it by 2 you get (6,8,10) which is also a pythagoras triplet.
Multiply it by 3 you get ( 9,12,15) which is also a pythagoras triplet.
Multiply it by 4 you get (12,16,20) which is also a pythagoras triplet.
You may multiply by any constant you will get a pythagoras triplet
Take another example (5,12,13)
Multiply it by 5,6 and 7 and check if you get a pythagoras triplet.

TIPS FOR SMART GUESSING :
You will notice that in any case, whether it is a unique triplet or it is a derived triplet (derived by multiplying a constant to a unique triplet), all the three numbers cannot be odd. 
In case of unique triplet , the hypotenuse is always odd and one of the remaining side is odd the other one is even.
Below are the first few unique triplets with first number as Odd.
3    4    5
5    12   13
7    24   25
9    40   41
11   60   61
You will notice following trend for unique triplets with first side as odd.
Hypotenuse = (Sq(first side) +1) / 2
Other side = Hypotenuse –1 or (first side * n + n)

Example : First side = 3 ,
so hypotenuse = (3*3+1)/2= 5 and other side = 5-1=4
Example 2: First side = 11
so hypotenuse = (9*9+1)/2= 41 and other side = 41-1=40

Please note that the above is not true for a derived  triplet for example 9,12 and 15, which has been obtained from multiplying 3 to the triplet of 3,4,5.  You may check for other derived triplets.
Below are the first few unique triplets with first number as Even .
4    3    5
8    15   17
12   35   37
16   63   65
20   99   101
You will notice following trend for unique triplets with first side as Even.
Hypotenuse = Sq( first side/ 2)+1
Other side = Hypotenuse-2

Example 1. First side =8
So hypotenuse = sq(8/2) +1= 17
Other side = 17-2=15
Example 2. First side = 16
So hypotenuse = Sq(16/2) +1 =65
Other side = 65-2= 63