In a [tex]\( 45^\circ - 45^\circ - 90^\circ \)[/tex] triangle, the properties of the triangle are well defined. Specifically, the legs of such a triangle are congruent (they have the same length), and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
Let's denote the length of each leg of the triangle as [tex]\( L \)[/tex]. According to the properties of a [tex]\( 45^\circ - 45^\circ - 90^\circ \)[/tex] triangle, the hypotenuse (H) can be expressed as:
[tex]\[ \text{H} = L \cdot \sqrt{2} \][/tex]
Given that the hypotenuse is [tex]\( 22 \sqrt{2} \)[/tex]:
[tex]\[ 22 \sqrt{2} = L \cdot \sqrt{2} \][/tex]
To find the leg length [tex]\( L \)[/tex], we can divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ L = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]
Since [tex]\( \sqrt{2} \)[/tex] in the numerator and denominator cancels out, we get:
[tex]\[ L = 22 \][/tex]
Therefore, the length of one leg of the triangle is [tex]\( 22 \)[/tex] units. Hence, the correct answer to the question is:
22 units
