Answer:
(B)
Step-by-step explanation:
The given options are:
A. 2, 2, [tex]\sqrt{42}[/tex]
B. 9,40, 41
C. [tex]\sqrt{5},10,\sqrt{125}[/tex]
In order to prove that the given side lengths form a right triangle, we will satisfy the Pythagoras theorem.
A. [tex](\sqrt{42})^{2}=(2)^{2}+(2)^{2}[/tex]
⇒[tex]42=4+4[/tex]
⇒[tex]42=8[/tex]
which does not satisfy the theorem, thus this option is incorrect.
B. [tex](41)^{2}=(9)^{2}+(40)^{2}[/tex]
⇒[tex]1681=1600+81[/tex]
⇒[tex]1681=1681[/tex]
which satisfies the theorem, thus this option is correct.
C. [tex](\sqrt{125})^{2}=(10)^{2}+(\sqrt{5})^{2}[/tex]
⇒[tex]125=100+5[/tex]
⇒[tex]125=105[/tex]
which does not satisfy the theorem, thus this option is incorrect.
