Sure, let's solve this step by step!
In a 45°-45°-90° triangle, we know that the lengths of the legs are equal, and each leg is related to the hypotenuse by a specific ratio. The specific relationship between the side length and the hypotenuse in a 45°-45°-90° triangle is given by the formula:
[tex]\[
\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}
\][/tex]
Given that the hypotenuse measures 18 cm, we can calculate the length of one leg as follows:
1. Determine the formula application:
The length of each leg in a 45°-45°-90° triangle can be calculated using the formula:
[tex]\[
\text{leg} = \frac{18 \, \text{cm}}{\sqrt{2}}
\][/tex]
2. Perform the division:
[tex]\[
\text{leg} = \frac{18}{\sqrt{2}}
\][/tex]
3. Simplify the expression:
Mathematically simplifying the division can yield more insight into the exact relationship and confirm if it's written in the simplest form. Normally, multiplying numerator and denominator by \(\sqrt{2}\) would help rationalize:
[tex]\[
\text{leg} = \frac{18 \sqrt{2}}{2} = 9 \sqrt{2}
\][/tex]
4. Calculate the numerical value:
Numerically evaluating the expression \(\frac{18}{\sqrt{2}}\) gives approximately 12.73 cm (not necessarily needing to reference the straightforward result).
Based on the calculations, the answer out of the options given is [tex]\(9 \sqrt{2} \, \text{cm}\)[/tex].
