HOW TO FIND THE OTHER TWO NUMBERS IN PYTHAGOREAN TRIPLET

One of the members of the Pythagorean Triplet is given below. Find the other numbers .

Problem 1 :

(6,----,-----)

Solution :

Since the numbers involving in this is even,

2m = 6

m = 3

The value of m is 3.

So, the required Pythagorean triple is 6, 8 and 10.

Problem 2 :

(9,----,---)

Solution :

m = 9 (odd)

So, the required Pythagorean triplet is (9, 40 and 41).

Problem 3 :

(-----,8,----)

Solution :

Since the numbers involving in this is even,

m² - 1 = 8

m² = 8 + 1

m² = 9

m = 3

So, the Pythagorean triplet is (6, 8 and 10).

Problem 4 :

(-------, 24,------)

Solution :

Since the numbers involving in this is even,

m² - 1 = 24

m² = 24 + 1

m² = 25

m = 5

So, the Pythagorean triplet is (10, 24 and 26).

Problem 5 :

Which of the following triplet is a Pythagorean Triplet:

a. (4, 5, 6)    b. (11, 60, 61)     c. (10, 8, 6)    d. both b and c

Solution :

Option a :

a = 4, b = 5 and c = 6

c² = a² + b²

6² = 4² + 5²

36 = 16 + 25

36 ≠ 41

So, option a is not Pythagorean triple.

Option b :

a = 11, b = 60 and c = 61

c² = a² + b²

61² = 11² + 60²

3721 = 121 + 3600

3721 = 3721

So, option b is Pythagorean triple.

Option c :

a = 10, b = 8 and c = 6

c² = a² + b²

10² = 8² + 6²

100 = 64 + 36

100 = 100

So, option c is Pythagorean triple.

Hence the correct answer is option d.

Problem 6 :

If m, n, p are natural numbers such that (m, n, p) forms a Pythagorean triplet if ?

a.  m²+n² = p²        b. m²+n² < p²        c. m²+n² > p²

d. m²+n² ≠ p²

Solution :

Considering the three natural numbers m, n and p, if they are Pythagorean triplet, it should satisfy the condition

m²+n² = p² 

Problem 7 :

Write a Pythagorean triplet whose one number is

a) 6     b) 14      c) 16

Solution :

a)  Since the given number is even, we can consider 2m = 6

m = 3

The other two numbers will be

m² - 1 and m² + 1

So, the required Pythagorean triple is (6, 8, 10).

b)  Since the given number is even, we can consider 2m = 14

m = 7

The other two numbers will be

m² - 1 and m² + 1

So, the required Pythagorean triple is (14, 48, 50).

c)  Since the given number is even, we can consider 2m = 16

m = 9

The other two numbers will be

m² - 1 and m² + 1

So, the required Pythagorean triple is (9, 80, 82).