Answer: The correct option is (A) 18 units.
Step-by-step explanation: We are given to find the length of the hypotenuse of the triangle in the figure.
Given in the figure that,
lengths of the two legs of the right-angled triangle are each 9√2 units,
So,
[tex]\textup{perpendicular, }p=9\sqrt2~\textup{units},\\\\\textup{base, }b=9\sqrt2~\textup{units}.[/tex]
Length of the hypotenuse, h = ?
Using Pythagoras theorem, we have from the given right-angled triangle,
[tex]\textup{hypotenuse}^2=\textup{perpendicualr}^2+\textup{base}^2\\\\\Rightarrow h^2=p^2+b^2\\\\\Rightarrow h^2=(9\sqrt2)^2+(9\sqrt2)^2\\\\\Rightarrow h^2=162+162\\\\\Rightarrow h^2=324\\\\\Rightarrow h=18~\textup{units}.[/tex]
Thus, the length of the hypotenuse is 18 units.
Option (A) is correct.
