Question

Check whether the following triplets are Pythagorean triplets. a) (10, 08, 21) b) (15, 07, 21) c) ( 30, 07, 21 )​

Answer 1

Answer:

ions

Which of the following triplets are Pythagorean?

(3,4,5),(6,7,8),(10,24,26),(2,3,4).

Answer

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Hint: For three numbers to be Pythagorean triplets, they should be in the form of (2m,m2−1,m2+1)

. In this question for the given triplets we will check whether the given triplets are in the form of (2m,m2−1,m2+1)

or not one by one and if they satisfy the following form then they are the Pythagorean triplets.

Here from the triplets an even number will be selected which will be equated to 2m

from which the value of m

will be calculated.

Complete step-by-step answer:

Given the triplets to be checked are

(3,4,5),(6,7,8),(10,24,26),(2,3,4).

Let the smallest even number be 2m

We will check each of the given set one by one

I.For (3,4,5)

Let 2m=4

Hence m=2

Now we will check for condition

m2−1=(2)2−1=4−1=3⇒m2+1=(2)2+1=4+1=5

Therefore we can say the triplet (3,4,5)

is a Pythagorean triplet.

II.Now for (6,7,8)

Let 2m=6

Hence m=3

Now we will check for condition

m2−1=(3)2−1=9−1=8⇒m2+1=(3)2+1=9+1=10

Therefore the triplet (6,7,8)

is not a Pythagorean triplet.

III.Now for (10,24,26)

Let 2m=10

Hence m=5

Now we will check for condition

m2−1=(5)2−1=25−1=24⇒m2+1=(5)2+1=25+1=26

Therefore the triplet (10,25,26)

is a Pythagorean triplet.

IV.Also for (2,3,4)

Let 2m=2

Hence m=1

Now we will check for condition

m2−1=(1)2−1=1−1=0m2+1=(1)2+1=1+1=2

Therefore the given triplets (10,25,26)

are the Pythagorean triplets.

Therefore from the given set of triplets (3,4,5)

and (10,25,26)

are the Pythagorean triplets.

So, the correct answer is “(3,4,5)

and (10,25,26)

Answer 2

Step-by-step explanation:

1) (21)^2= (10)^2+(8)^2

441= 100+64

441=164 Not a Triplet

2) (21)^2=(15)^2+(7)^2

441= 225+49

441= 274

not a Triplet

3) (30)^2= (21)^2+(7)^2

900= 441+49

900= 490

Not a Triplet