Question

which of the following could represent lengths of the sides of a right triangle? select all that apply.
5, 12, 15
√6, √10, 4
8, √28, √74
6, 8, 10
48, 55, 63

Explanation:

Step1: Check the Pythagorean theorem for \(9, 12, 15\)

$$9^{2}+12^{2}=81 + 144=225=15^{2}$$

Step2: Check the Pythagorean theorem for \(\sqrt{6},\sqrt{10},x\)

$$(\sqrt{6})^{2}+(\sqrt{10})^{2}=6 + 10=16=4^{2}$$

Step3: Check the Pythagorean theorem for \(9,72,75\)

$$9^{2}+72^{2}=81+5184 = 5265 eq75^{2}=5625$$

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

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

Step5: Check the Pythagorean theorem for \(48,55,63\)

$$48^{2}+55^{2}=2304+3025 = 5329 eq63^{2}=3969$$

Answer:

\(9, 12, 15\), \(\sqrt{6},\sqrt{10},4\), \(6,8,10\)