To find the length of one leg of a 45°-45°-90° triangle when the hypotenuse is given, follow these steps:
1. Understand the properties of a 45°-45°-90° triangle:
- In a 45°-45°-90° triangle, the legs are congruent (equal in length).
- The relationship between the legs and the hypotenuse is expressed using the formula:
[tex]\[
\text{hypotenuse} = \text{leg} \times \sqrt{2}
\][/tex]
2. Given information:
- Hypotenuse = [tex]\( 22\sqrt{2} \)[/tex] units
3. Set up the equation based on the triangle properties:
- Let [tex]\( l \)[/tex] be the length of one leg.
- According to the properties, we have:
[tex]\[
\text{hypotenuse} = l \times \sqrt{2}
\][/tex]
- Substitute the given hypotenuse into the equation:
[tex]\[
22\sqrt{2} = l \times \sqrt{2}
\][/tex]
4. Solve for [tex]\( l \)[/tex]:
- To isolate [tex]\( l \)[/tex], divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[
l = \frac{22\sqrt{2}}{\sqrt{2}}
\][/tex]
- Simplifying the expression on the right-hand side:
[tex]\[
l = 22
\][/tex]
Thus, the length of one leg of the triangle is [tex]\( 22 \)[/tex] units. This matches the option "22 units."
