Question

1. which set of numbers does not represent the sides of a right triangle?
2. (6,8,10)
3. (8,15,17)
4. (8,24,25)
5. (15,36,39)

Explanation:

Step1: Apply Pythagorean theorem

For a set of numbers \((a,b,c)\) to be sides of a right - triangle, \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the longest side).
For set (1) \((6,8,10)\):
\(6^{2}+8^{2}=36 + 64=100\) and \(10^{2}=100\). So \(6^{2}+8^{2}=10^{2}\).
For set (2) \((8,15,17)\):
\(8^{2}+15^{2}=64+225 = 289\) and \(17^{2}=289\). So \(8^{2}+15^{2}=17^{2}\).
For set (3) \((8,24,25)\):
\(8^{2}+24^{2}=64 + 576=640\) and \(25^{2}=625\). Since \(8^{2}+24^{2}
eq25^{2}\).
For set (4) \((15,36,39)\):
\(15^{2}+36^{2}=225+1296 = 1521\) and \(39^{2}=1521\). So \(15^{2}+36^{2}=39^{2}\).

Answer:

\((8,24,25)\) (i.e., option 3) does not represent the sides of a right - triangle.