Question

Identify the given triplets are Pythagorean or not (i) 6,7,8 (ii) 12,35,37 (iii) 12,21,24​

Answer 1

Answer:

(1). 6,7,8

largest number is 8

we observe that 8^2 is not equal to 6^2+7^2

so it is not a Pythagorean triplet.

(2) 12,35,37

largest number is 37

we observe that 37^2 = 12^2+35^2

so it is a Pythagorean triplet.

(3). 12,21,24

largest number= 24

we observe that 12^2+21^2 is not equal to24^2

so it is not a Pythagorean triplet.

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Answer 2

Answer:

(i) No

(ii) Yes

(iii) No

Explanation:

We know that, in Pythagorean triplet the square of biggest number is equal to the sum of squares of other two numbers. So, according to theorem,

(i) (8)^2 = (6)^2 + (7)^2

=> 64 = 36 + 49

=> 64 ≠ 85

So it is not a Pythagorean triplet.

(ii) (37)^2 = (12)^2 + (35)^2

=> 1369 = 144 + 1225

=> 1369 = 1369

Hence, it is a Pythagorean triplet.

(iii) (24)^2 = (12)^2 + (21)^2

=> 576 = 144 + 441

=> 576 ≠ 585

Hence, it is not a Pythagorean triplet.