Question
For the pair of numbers, find a third whole number such that the three numbers form a Pythagorean triple.
20, 48
Question content area bottom
Part 1
The third number of the Pythagorean triple is
enter your response here.
(Type a whole number.)
20, 48
Question content area bottom
Part 1
The third number of the Pythagorean triple is
enter your response here.
(Type a whole number.)
Answers
GPT-4o mini
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 \( (20, 48, 52) \).
\[ a^2 + b^2 = c^2 \]
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 \( (20, 48, 52) \).