To find the length of one leg of a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle when the hypotenuse is given, we start by recalling a key property of such triangles. In a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle, the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of each leg.
Given that the hypotenuse is [tex]\(22\sqrt{2}\)[/tex] units, let's denote the length of one leg as [tex]\(x\)[/tex]. According to the triangle's properties, we have the relationship:
[tex]\[ \text{hypotenuse} = x \times \sqrt{2} \][/tex]
Substituting the given hypotenuse into the equation:
[tex]\[ 22\sqrt{2} = x \times \sqrt{2} \][/tex]
Next, we solve for [tex]\(x\)[/tex]. To isolate [tex]\(x\)[/tex], we can divide both sides of the equation by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \frac{22\sqrt{2}}{\sqrt{2}} = x \][/tex]
Since [tex]\(\sqrt{2}\)[/tex] in the numerator and the denominator cancel each other out, we get:
[tex]\[ x = 22 \][/tex]
So, the length of one leg of the triangle is [tex]\(22\)[/tex] units.
Therefore, the correct answer is:
22 units
