To find the length of one leg of a 45°-45°-90° triangle when the hypotenuse is given, it's important to understand the special properties of this type of triangle. In a 45°-45°-90° triangle, the legs are equal in length, and the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of one leg.
Given that the hypotenuse measures [tex]\(22 \sqrt{2}\)[/tex] units, we can use this relationship to determine the length of one leg.
1. Let [tex]\(x\)[/tex] be the length of one leg of the triangle.
2. According to the properties of a 45°-45°-90° triangle, the hypotenuse [tex]\(c\)[/tex] is related to the leg [tex]\(x\)[/tex] by the formula:
[tex]\[ c = x \sqrt{2} \][/tex]
3. Plugging in the given hypotenuse value:
[tex]\[ 22 \sqrt{2} = x \sqrt{2} \][/tex]
4. To isolate [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ x = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]
5. Simplifying the fraction on the right-hand side, [tex]\(\sqrt{2}\)[/tex] cancels out:
[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
