The triangle in question is a 45°-45°-90° triangle. This specific type of triangle has special properties that relate the lengths of the legs to the hypotenuse.
### Properties of a 45°-45°-90° Triangle
- The two legs are congruent (equal in length).
- The length of the hypotenuse is equal to the length of one leg multiplied by [tex]\(\sqrt{2}\)[/tex].
Given:
- Hypotenuse [tex]\( = 22\sqrt{2} \)[/tex] units
Let [tex]\( x \)[/tex] be the length of each leg of the triangle.
### Relationship between Hypotenuse and Legs of a 45°-45°-90° Triangle
The relationship can be expressed as:
[tex]\[ \text{Hypotenuse} = x \cdot \sqrt{2} \][/tex]
### Substitute the Given Value:
[tex]\[ 22\sqrt{2} = x \cdot \sqrt{2} \][/tex]
### Solve for [tex]\( x \)[/tex]:
Divide both sides by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ x = \frac{22\sqrt{2}}{\sqrt{2}} \][/tex]
### Simplify:
[tex]\[ x = 22 \][/tex]
### Conclusion
So, the length of one leg of the triangle is [tex]\( \boxed{22} \)[/tex] units.
