Question

which of the following triplets are Pythagorean? a) <2,2,5> b) <2,3,4> c) <3,4,5> d) <6,8,10> e) <12,35,37>

Answer 1

c d and e are the answers

hope it helps you

in Pythagoras theorem sum of square of two smallest sides is equal to square of the biggest size


hence in c smallest sides are 3 and 4
therefore 9+16=25
longest side is 5
therefore 25
hence proved

same rule applies in d and e

Answer 2

a) 2,2,5
2²=4 , 2²=4, 5²=25
2²+2²=4+4=8
8≠25
2²+2²=5²
Therefore, 2,2,5 do not form a Pythagorean triplet.

b) 2,3,4
2²=4 , 3²=9 , 4² = 16
2²+3³=4+9=13
13≠16
2²+3²≠4²
Therefore, 2,3,4 do not form a Pythagorean triplet.

c) 3,4,5
3²=9 , 4²=16 , 5²=25
3²+4²=9+16=25
25=25
3²+4²=5²
therefore, 3,4,5 form a Pythagorean triplet.

d) 6,8,10
6²=36 , 8²=64 , 10²=100
6²+8²=36+64=100
100=100
6²+8²=10²
therefore, 6,8,10 forms a Pythagorean triplet.

e)12,35,37
12²=144 , 35²=1225 , 37²=1369
12²+35²=144+1225=1369
1369=1369
12²+35²=37²
therefore, 12,35,37 forms a Pythagorean triplet.


Therefore, C,D,E forms a Pythagorean triplet.