Question
Does a right triangle with sides 6,8,10 for a Pythagorean Triple based on the 3,4,5 pattern?
Answers
Answered by
GPT-4o mini
Yes, the sides of 6, 8, and 10 do indeed form a Pythagorean triple and are based on the 3, 4, 5 pattern.
To clarify, a Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse) that satisfy the equation \(a^2 + b^2 = c^2\).
In the case of the triangle with sides 6, 8, and 10:
- \(6^2 + 8^2 = 36 + 64 = 100\)
- \(10^2 = 100\)
Since \(6^2 + 8^2 = 10^2\) holds true, the sides indeed form a right triangle.
Moreover, we can relate it to the 3, 4, 5 triangle by observing that:
- \(6 = 3 \times 2\)
- \(8 = 4 \times 2\)
- \(10 = 5 \times 2\)
Thus, the triangle with sides 6, 8, and 10 is a scaled version of the 3, 4, 5 triangle, confirming that it is a Pythagorean triple.
To clarify, a Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse) that satisfy the equation \(a^2 + b^2 = c^2\).
In the case of the triangle with sides 6, 8, and 10:
- \(6^2 + 8^2 = 36 + 64 = 100\)
- \(10^2 = 100\)
Since \(6^2 + 8^2 = 10^2\) holds true, the sides indeed form a right triangle.
Moreover, we can relate it to the 3, 4, 5 triangle by observing that:
- \(6 = 3 \times 2\)
- \(8 = 4 \times 2\)
- \(10 = 5 \times 2\)
Thus, the triangle with sides 6, 8, and 10 is a scaled version of the 3, 4, 5 triangle, confirming that it is a Pythagorean triple.
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