Question

which lengths would form a right triangle?
24, 7, and 26
9, 12, and 14
21, 16, and 12
30, 24, and 18

Explanation:

Step1: Apply Pythagorean theorem

For a set of side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), check if \(a^{2}+b^{2}=c^{2}\)

For \(24\), \(7\), \(26\)

• Calculate \(24^{2}+7^{2}=576 + 49=625\)
• Calculate \(26^{2}=676\)
• Since \(625

eq676\), these do not form a right - triangle

For \(9\), \(12\), \(14\)

• Calculate \(9^{2}+12^{2}=81+144 = 225\)
• Calculate \(14^{2}=196\)
• Since \(225

eq196\), these do not form a right - triangle

For \(21\), \(16\), \(12\)

• Here \(21\) is the longest side
• Calculate \(16^{2}+12^{2}=256+144 = 400\)
• Calculate \(21^{2}=441\)
• Since \(400

eq441\), these do not form a right - triangle

For \(30\), \(24\), \(18\)

• Here \(30\) is the longest side
• Calculate \(24^{2}+18^{2}=576+324=900\)
• Calculate \(30^{2}=900\)
• Since \(24^{2}+18^{2}=30^{2}\), these form a right - triangle

Answer:

\(30\), \(24\), and \(18\)