Question

fill in the blanks to make each a Pythagorean triplet 5,_,_​

Answer 1

Answer:

The Pythagorean triplet are 5,4,3.

Step-by-step explanation:

Consider the provided statement.

The Pythagorean triplet are in the form of $2m ,m^2 -1\ \text{and}\ m^2+1$.

Where, the value of m should be a natural number.

It is given that one number of triplet is 5 therefore.

2m = 5

m = 5/2

Which is not a natural number.

Let $m^2-1=5$ then,

$m^2=5+1$

$m^2=6$

Which is not a natural number.

Let $m^2+1=5$ then,

$m^2=5-1$

$m^2=4$

$m=\pm2$

Ignore the negative value as side can not be a negative number.

Therefore the value of m is 2 now substitute the this value in Pythagorean triplet.

$2(2), (2)^2 -1\ \text{and}\ (2)^2+1$

$4, 4 -1\ \text{and}\ 4+1$

$4, 3\ \text{and}\ 5$

Therefore, the Pythagorean triplet are 5,4,3.