Certainly! Let's solve the problem step by step.
We are dealing with a [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle. In this type of triangle, the legs are of equal length, and the hypotenuse is \( \sqrt{2} \) times the length of each leg.
Given:
- Each leg of the triangle measures \( 12 \) cm.
To find the length of the hypotenuse, we use the relationship specific to a [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle:
[tex]\[ \text{Hypotenuse} = \text{leg} \times \sqrt{2} \][/tex]
Substituting the given leg length:
[tex]\[ \text{Hypotenuse} = 12 \, \text{cm} \times \sqrt{2} \][/tex]
Now, calculate the result:
[tex]\[ \text{Hypotenuse} = 12 \sqrt{2} \, \text{cm} \][/tex]
Thus, the length of the hypotenuse is:
[tex]\[ 12 \sqrt{2} \, \text{cm} \][/tex]
So the correct choice from the given options is:
[tex]\[ \boxed{12 \sqrt{2} \, \text{cm}} \][/tex]
