Question

Find the Pythagorean triplet whose one number is
a)10
b)15
c)50

Answer 1

Hint: To answer this type of problem we have to use the Pythagorean theorem and find the numbers. In this problem one number is given and the other two numbers can be found by applying the Pythagorean theorem and finding which other two numbers satisfy the condition of pythagoras theorem. Those numbers will be the another two numbers.

Complete step-by-step answer:
Part (a):
In part a 10 is given as a first number and we have to find two other numbers.
Now find the square of 10 it will be equal to 100.
Now think any two numbers squares sum which is equal to 100.
If take 6 and 8
\[{6^2} + {8^2} = {10^2}\]
We see the sum of squares of the number 6 and 8 gives 100
Hence the triplet of 10 Pythagorean triplet of 10 is 6 and 8
Hence triplets 6,8,10
Part (b):
In part b 15 is given as a first number and we have to find two other numbers.
Now find the square of 15 it will be equal to 225.
Now think of any number whose square sum with square of 15 is equal to square of 17.
If take 8 check the Pythagorean triplet condition we see it is valid.
\[{8^2} + {15^2} = {17^2}\]
Hence triplets 8,15,17
Part (c):
In part a 50 is given as a first number and we have to find two other numbers.
Now find the square of 50 it will be equal to 2500.
Now think any two numbers squares sum which is equal to 2500.
If take 20 and 40
\[{30^2} + {40^2} = {50^2}\]
We see the sum of squares of the number 20 and 40 gives 2500
Hence triplets 30, 40, 50

Note: Triplets means always three things together. In this problem it says Pythagorean triplets means any three numbers which can satisfy the pythagorean theorem. So students do not be confused.