To determine which of the given sets of numbers is not a Pythagorean triplet, we need to check whether each set satisfies the Pythagorean theorem. A Pythagorean triplet consists of three positive integers \(a\), \(b\), and \(c\), such that \(a^2 + b^2 = c^2\), where \(c\) is the largest number.
- For the set 20, 99, 100:
- Identify the largest number: \(c = 100\).
- Apply the Pythagorean theorem: \(20^2 + 99^2 = 400 + 9801 = 10201\) and \(100^2 = 10000\).
- Since \(10201 \neq 10000\), this set does not satisfy the Pythagorean theorem.
- For the set 8, 15, 17:
- Identify the largest number: \(c = 17\).
- Apply the Pythagorean theorem: \(8^2 + 15^2 = 64 + 225 = 289\) and \(17^2 = 289\).
- Since \(289 = 289\), this is a Pythagorean triplet.
- For the set 12, 35, 37:
- Identify the largest number: \(c = 37\).
- Apply the Pythagorean theorem: \(12^2 + 35^2 = 144 + 1225 = 1369\) and \(37^2 = 1369\).
- Since \(1369 = 1369\), this is a Pythagorean triplet.
- For the set 20, 21, 29:
- Identify the largest number: \(c = 29\).
- Apply the Pythagorean theorem: \(20^2 + 21^2 = 400 + 441 = 841\) and \(29^2 = 841\).
- Since \(841 = 841\), this is a Pythagorean triplet.
Thus, the set 20, 99, 100 is not a Pythagorean triplet as it does not satisfy the condition \(a^2 + b^2 = c^2\).
Similar Questions
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$AB = 36\text{ cm}$
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$BC = 48\text{ cm}$
Triangle $PQR$ have the following sides:
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$PR = 5\text{ cm}$
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Among the following options, which are NOT sides of a triangle?
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