Question

which cannot be used as side lengths of a ri
(3,4,5)
(5,12,13
(8,15,17
(6,8,10)

Explanation:

Step1: Check Pythagorean theorem for (3,4,5)

$$3^{2}+4^{2}=9 + 16=25=5^{2}$$

Step2: Check Pythagorean theorem for (5,12,13)

$$5^{2}+12^{2}=25+144 = 169=13^{2}$$

Step3: Check Pythagorean theorem for (8,15,17)

$$8^{2}+15^{2}=64 + 225=289=17^{2}$$

Step4: Check Pythagorean theorem for (6,8,10)

$$6^{2}+8^{2}=36+64 = 100=10^{2}$$

Answer:

None of them. All the given sets \((3,4,5)\), \((5,12,13)\), \((8,15,17)\), \((6,8,10)\) satisfy the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the longest side) and can be used as side lengths of a right - triangle.