Which of the following triplets are Pythagorean? (I)`(8,\ 15 , 17)` (ii) `(18 ,\ 80 , 82)` (iii)`(14 , 48 , 51)` (iv) `(10 , 24 , 26)` (v)`(16 , 63 , 65)` (vi) `(12 , 35 , 38)`

Explanation

Sum of the squares of two smallest numbers is equal to the square of largest number is known as Pythagorean triplet. The triplets which satisfies the given statements are:
(i)`(8,15,17)`: `8^2+15^2=17^2rArr64+225=289`

(ii)`(18,80,82)`: `18^2+80^2=82^2rArr324+6400=6724`

(iv)`(10,24,26)`: `10^2+24^2=26^2rArr100+576=676`

(v)`(16,63,65)`: `16^2+63^2=65^2rArr256+3969=4225`

The triplets which does not satisfies the given statement are:

(iii) `(14,48,51): 14^2+48^2ne51^2rArr196+2304ne2601`

(vi) `(12,35,38): 12^2+35^2ne38^2rArr144+1225ne1444`