Question

if (16,x,65) a Pythagorean triplet with 16<x<65, then find the value of x

Answer 1

HEYA!!
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✴PYTHAGOREAN TRIPLET✴
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Given that 16, x and 65 are the members of the Pythagorean triplet ..

Also x is the intermediate term ,

The members of a Pythagorean triplet are represented by

$= > > 2m \: \: m {}^{2} + 1 \: \: and \: m {}^{2} - 1$
Here the smallest member is 16

✴ 2m = 16

m = 8

$m {}^{2} + 1 = 8 {}^{2} + 1 \\ \\ = > > 64 + 1 = 65 \\ \\ \\ x = > m {}^{2} - 1 \\ \\ = 64 - 1 = 63$
Hence the triplet is 16, 63 and 65 .

Hence x =63

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Answer 2

in Pythagorean triplet the square of bigger number is equal to the sum of other two number
(16)^2+x^2=(65)^2
256+x^2=4225
x^2=4225-256
x^2=3969
x=63......taking square root on both the side