Let's solve the problem in a step-by-step manner:
Given:
- The hypotenuse of a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle measures [tex]\( 22 \sqrt{2} \)[/tex] units.
In a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle, the sides have a specific ratio relative to each other. The legs of such a triangle are equal, and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
To find the length of one of the legs, we use the property of this special triangle:
1. Let the length of each leg be [tex]\( x \)[/tex].
2. Since the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the leg, we have:
[tex]\[
\text{Hypotenuse} = x \sqrt{2}
\][/tex]
3. We know the hypotenuse is [tex]\( 22 \sqrt{2} \)[/tex] units, so:
[tex]\[
22 \sqrt{2} = x \sqrt{2}
\][/tex]
4. To find [tex]\( x \)[/tex], we divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[
x = \frac{22 \sqrt{2}}{\sqrt{2}}
\][/tex]
5. Simplify the right-hand side:
[tex]\[
x = 22
\][/tex]
Thus, the length of one leg of the triangle is [tex]\( 22 \)[/tex] units.
Therefore, the correct option is:
- 22 units
