Sure! Let's solve this step-by-step.
We are given a [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle, which is also known as an isosceles right triangle. One of the distinctive properties of this type of triangle is that the two legs are congruent, meaning they have the same length. Additionally, the relationship between the legs and the hypotenuse in a [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle is known and can be described as follows:
- The length of each leg is the hypotenuse divided by [tex]$\sqrt{2}$[/tex].
Given that the hypotenuse measures [tex]$22 \sqrt{2}$[/tex] units, we can determine the length of one leg using this relationship.
1. We start with the length of the hypotenuse:
[tex]\[ \text{Hypotenuse} = 22 \sqrt{2} \text{ units} \][/tex]
2. To find the length of one leg, we divide the hypotenuse by [tex]$\sqrt{2}$[/tex]:
[tex]\[ \text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]
3. We simplify the fraction:
[tex]\[ \text{Leg} = \frac{22 \sqrt{2}}{\sqrt{2}} = 22 \][/tex]
Thus, the length of one leg of the triangle is 22 units. The correct answer is:
22 units
