Answer:
Option C.
Step-by-step explanation:
Given information: The hypotenuse of a 45°-45°-90° triangle measures 22√2 units.
Let x be the length of one leg.
From the given figure it is clear that length of both legs are same.
According to the Pythagoras theorem, in a right angled triangle
[tex](leg_1)^2+(leg_2)^2=hypotenuse^2[/tex]
Substitute [tex]leg_1=leg_2=x, hypotenuse=22\sqrt{2}[/tex] in the above formula.
[tex](x)^2+(x)^2=(22\sqrt{2})^2[/tex]
[tex]2x^2=(22)^2(\sqrt{2})^2[/tex]
[tex]2x^2=2(22)^2[/tex]
Divide both sides by 2.
[tex]x^2=(22)^2[/tex]
Taking square root on both sides.
[tex]x=22[/tex]
The length of one leg is 22 units.
Therefore, the correct option is C.
