Does the set of numbers form a Pythagorean​ triple? Explain.

Question

60 comma 45 comma 75
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Part 1
Choose the correct answer below.
No​, because the given numbers satisfy the equation a squared plus b squared equals c squared.
No​, because the given numbers do not satisfy the equation a squared plus b squared equals c squared.
Yes​, because the given numbers do not satisfy the equation a squared plus b squared equals c squared.
Yes​, because the given numbers satisfy the equation a squared plus b squared equals c squared.

Answer 1

To determine whether the numbers 60, 45, and 75 form a Pythagorean triple, we can check if they satisfy the condition \(a^2 + b^2 = c^2\), where \(c\) is the largest number.

1. Identify the values:

   • \(a = 45\)
   • \(b = 60\)
   • \(c = 75\)

2. Calculate \(a^2 + b^2\): \[ a^2 = 45^2 = 2025 \] \[ b^2 = 60^2 = 3600 \] \[ a^2 + b^2 = 2025 + 3600 = 5625 \]

3. Calculate \(c^2\): \[ c^2 = 75^2 = 5625 \]

4. Compare \(a^2 + b^2\) with \(c^2\): \[ a^2 + b^2 = c^2 \implies 5625 = 5625 \]

Since \(a^2 + b^2 = c^2\) is true, the numbers 60, 45, and 75 do indeed form a Pythagorean triple.

The correct answer is: Yes, because the given numbers satisfy the equation \(a^2 + b^2 = c^2\).