Question

determine which set of side measurements could be used to form a right triangle.
√2, √3, 5
√2, 3, √11
7, 9, 11
5, 10, 14

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
For the set \(\sqrt{2},3,\sqrt{11}\):
\((\sqrt{2})^{2}+3^{2}=2 + 9=11\)
\((\sqrt{11})^{2}=11\)

Step2: Check other sets

For the set \(\sqrt{2},\sqrt{3},5\): \((\sqrt{2})^{2}+(\sqrt{3})^{2}=2 + 3=5
eq25 = 5^{2}\)
For the set \(7,9,11\): \(7^{2}+9^{2}=49+81 = 130
eq121=11^{2}\)
For the set \(5,10,14\): \(5^{2}+10^{2}=25 + 100=125
eq196 = 14^{2}\)

Answer:

\(\sqrt{2},3,\sqrt{11}\)