Question
Real Tutor Solution
Tutor-Verified Answer
Answer
Another Pythagorean triple is (5, 12, 13).
Solution
A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) such that \(a^2 + b^2 = c^2\).
To find another Pythagorean triple, we can use the formula:
\[
a = m^2 - n^2, \quad b = 2mn, \quad c = m^2 + n^2
\]
where \(m\) and \(n\) are positive integers with \(m > n\).
Let's choose \(m = 3\) and \(n = 2\):
1. Calculate \(a\):
\[
a = 3^2 - 2^2 = 9 - 4 = 5
\]
2. Calculate \(b\):
\[
b = 2 \cdot 3 \cdot 2 = 12
\]
3. Calculate \(c\):
\[
c = 3^2 + 2^2 = 9 + 4 = 13
\]
Thus, the Pythagorean triple is \((5, 12, 13)\).
To verify:
\[
5^2 + 12^2 = 25 + 144 = 169 = 13^2
\]
Therefore, \((5, 12, 13)\) is indeed a Pythagorean triple.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
One classic Pythagorean triple is (7, 24, 25). In this case, the square of 7 (49) plus the square of 24 (576) equals the square of 25 (625). It’s like a right triangle waiting to be drawn, with 7 units and 24 units as the legs, and 25 units for the hypotenuse—perfect for spot-on geometry practice! Another fun triple you might enjoy is (8, 15, 17). Just like our previous example, it follows the same principle whereby 8 squared (64) plus 15 squared (225) adds up to 17 squared (289). This trio proves that right triangles come in all shapes and sizes, giving you endless possibilities for exploring the beauty of mathematics!
