To determine which of the given options is not a Pythagorean triple, we need to check each option by verifying the Pythagorean theorem, which states that for a set of three numbers \(a\), \(b\), and \(c\) (where \(c\) is the largest), the following must hold true:
\[
c^2 = a^2 + b^2
\]
Let's go through the options step by step.
### Step 1: Identify the options
Assuming the options are:
1. (8, 15, 17)
2. (11, 60, 63)
3. (13, 84, 85)
4. (7, 24, 25)
### Step 2: Check each option
#### Option 1: (8, 15, 17)
- Here, \(c = 17\), \(a = 8\), and \(b = 15\).
- Calculate \(c^2\):
\[
17^2 = 289
\]
- Calculate \(a^2 + b^2\):
\[
8^2 + 15^2 = 64 + 225 = 289
\]
- Since \(c^2 = a^2 + b^2\), this is a Pythagorean triple.
#### Option 2: (11, 60, 63)
- Here, \(c = 63\), \(a = 11\), and \(b = 60\).
- Calculate \(c^2\):
\[
63^2 = 3969
\]
- Calculate \(a^2 + b^2\):
\[
11^2 + 60^2 = 121 + 3600 = 3721
\]
- Since \(c^2 \neq a^2 + b^2\), this is **not** a Pythagorean triple.
#### Option 3: (13, 84, 85)
- Here, \(c = 85\), \(a = 13\), and \(b = 84\).
- Calculate \(c^2\):
\[
85^2 = 7225
\]
- Calculate \(a^2 + b^2\):
\[
13^2 + 84^2 = 169 + 7056 = 7225
\]
- Since \(c^2 = a^2 + b^2\), this is a Pythagorean triple.
#### Option 4: (7, 24, 25)
- Here, \(c = 25\), \(a = 7\), and \(b = 24\).
- Calculate \(c^2\):
\[
25^2 = 625
\]
- Calculate \(a^2 + b^2\):
\[
7^2 + 24^2 = 49 + 576 = 625
\]
- Since \(c^2 = a^2 + b^2\), this is a Pythagorean triple.
### Conclusion
The option that is not a Pythagorean triple is **Option 2: (11, 60, 63)**.
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