In a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle, the legs are of equal length. The relationship between the length of a leg (let’s denote it as [tex]\( x \)[/tex]) and the hypotenuse (denoted as [tex]\( h \)[/tex]) in such a triangle is given by the formula:
[tex]\[ h = x\sqrt{2} \][/tex]
Given that the hypotenuse [tex]\( h \)[/tex] is [tex]\( 22\sqrt{2} \)[/tex] units, we can use this relationship to find the length of one leg.
Follow these steps:
1. Start with the relationship:
[tex]\[ h = x\sqrt{2} \][/tex]
2. Substitute the given hypotenuse value:
[tex]\[ 22\sqrt{2} = x\sqrt{2} \][/tex]
3. 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]
4. Simplify the fraction:
[tex]\[ x = 22 \][/tex]
Therefore, the length of one leg of the triangle is [tex]\( 22 \)[/tex] units.
So, the correct answer is:
22 units
