Question

How many of the following are Pythagorean triplets ?
[8, 15, 17], [13, 60, 61], [14, 48, 50). [11, 40, 41).
Explain it!!!!​

Answer 1

Question :-

To find which of the following are Pythagorean triplets.

Answer :-

Concept :-

According to the Pythagorean triplet, the three numbers are in the form as follows :-

• 2m
• m² - 1
• m² + 1

2m being the smallest number

Option 1 :-

➵ 8,15,17

In this set, 8 is the smallest number.

Therefore,

→ 2m = 8

→ m = 8 ÷ 2

→ m = 4

Now that we have the value of m, the other 2 numbers will be :-

→ m² - 1

→ (4)² - 1

→ 16 - 1

→ 15

The third number :-

→ m² + 1

→ (4)² + 1

→ 16 + 1

→ 17

All the answer's are matching the set. Hence, 8,15,17 is a Pythagorean triplet.

Option 2 :-

➵ 13,60,61

Here, the smallest number is 13.

→ 2m = 13

13 is not exactly divisible by 2. Hence this triplet cannot be formed.

Option 3 :-

➵ 14,48,50

Here 14, is the smallest number.

Therefore,

→ 2m = 14

→ m = 14 ÷ 2

→ m = 7

Second number :-

→ m² - 1

→ (7)² - 1

→ 49 - 1

→ 48

Third number :-

→ m² + 1

→ (7)² + 1

→ 49 + 1

→ 50

All the numbers are matching the set, hence 14,48,50 is a Pythagorean triplet

Option 4 :-

➵ 11,40,41

→ 2m = 11

Here 11 is not exactly divisible by 2. Hence the triplet cannot be formed.

Answer 2

Answer:

(1) 8^2 +15^2 = 17 ^2

64+225 =279

279 = 279

Hence,this prove that it is phythagorean triplet.

(2) 13^2 + 60^2 = 61^2

169+3600= 3721

Hence, this is not phythogorean triplet.

(3) 14^2+48^2=50^2

196+2304 =2500

2500 = 2500

Hence,this prove that it is phythagorean triplet .

(4) 11^2+40^2=41^2

121+1600=1681

1721= 1681

Hence,this is not phythagorean triplet.

Hence, the 1) 8^2+15^2=17^2 &

2) 14^2+48^2=50^2 are the phythogorean triplet.

Hence,the option [3] 2 is correct