Question

For the pair of​ numbers, find a third whole number such that the three numbers form a Pythagorean triple.
20​, 48
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Part 1
The third number of the Pythagorean triple is
  
enter your response here.
​(Type a whole​ number.)

Answer 1

To find a third whole number that, together with 20 and 48, forms a Pythagorean triple, we can use the Pythagorean theorem, which states that for a right triangle with sides \( a \), \( b \) and hypotenuse \( c \):

\[ a^2 + b^2 = c^2 \]

We can try to determine whether 20 or 48 should be used as the hypotenuse. However, since \( 20^2 + 48^2 \) will give a larger number, we will calculate:

1. Calculate \( 20^2 + 48^2 \):
\[
20^2 = 400
\]
\[
48^2 = 2304
\]
\[
20^2 + 48^2 = 400 + 2304 = 2704
\]

2. Now, find \( c \) (hypotenuse) such that:
\[
c^2 = 2704
\]
\[
c = \sqrt{2704} = 52
\]

Thus, the third whole number that forms a Pythagorean triple with 20 and 48 is:

\[
\boxed{52}
\]

So the triple is \( (20, 48, 52) \).