Which of the following triplets are Pythagorean?
a. (7,8,9)
b. (10,11,15) c. (6,8,10)
d. (10,24,25)
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Answer:
c. (6,8,10)
Step-by-step explanation:
a. (7,8,9)
a^2+b^2=c^2
7^2+8^2=9^2
49+64 =113 which is not equal to 81
So , here a^2+b^2 is not equal to c^2
b. (10,11,15)
a^2+b^2=c^2
10^2+11^2=15^2
100+121= 221 which is not equal to 225
So , here a^2+b^2 is not equal to c^2
c. (6,8,10)
a^2+b^2=c^2
6^2+8^2=10^2
36+64=100 which is equal to 100
So , here a^2+b^2 is equal to c^2
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Given : Triplets
a. (7,8,9)
b. (10,11,15)
c. (6,8,10)
d. (10,24,25)
To Find : Pythagorean triplet
Solution:
Pythagorean triplet ( a , b , c)
where c > a , b is given by c² = a² + b²
a. (7,8,9)
9² ≠ 7² + 8²
as 81 ≠ 113
b. (10,11,15)
15² ≠ 11² + 10²
as 225 ≠ 221
c. (6,8,10)
10² = 6² + 8²
as 100 ≠ 100
d. (10,24,25)
25² ≠ 24² + 10²
as 625 ≠ 676
Hence (6,8,10) is the Pythagorean triplet
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