To determine the length of one leg of a [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle whose hypotenuse measures 18 cm, let's follow these steps:
1. Understand the properties of a [tex]\( 45^\circ-45^\circ-90^\circ \)[/tex] triangle: In this type of triangle, both legs are of equal length, and the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of one leg.
2. Express the relationship mathematically: If the length of one leg is [tex]\( x \)[/tex], then the relationship can be written as:
[tex]\[
\text{hypotenuse} = x \sqrt{2}
\][/tex]
3. Substitute known values: Given that the hypotenuse is 18 cm, we have:
[tex]\[
18 = x \sqrt{2}
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{18}{\sqrt{2}}
\][/tex]
5. Simplify the expression: To make it simpler:
[tex]\[
x = 18 \cdot \frac{1}{\sqrt{2}} = 18 \cdot \frac{\sqrt{2}}{2} = 18 \cdot 0.70710678118 \approx 12.72792206136 \, \text{cm}
\][/tex]
Thus, the length of one leg of the triangle is approximately 12.72792206136 cm.
Therefore, the correct answer is not represented exactly in any of the given options. However, if it needs precise accuracy, the length of one leg is approximately 12.72792206136 cm.
