In a 45°-45°-90° triangle, each leg of the triangle is congruent, which means both legs have the same length. Let's denote the length of each leg as [tex]\(12 \, \text{cm}\)[/tex].
In such a triangle, the hypotenuse can be calculated using the properties of the 45°-45°-90° triangle, which is an isosceles right triangle. The hypotenuse (the side opposite the right angle) is always [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
Given:
- Each leg of the triangle [tex]\(= 12 \, \text{cm}\)[/tex]
To find the hypotenuse, you use the formula:
[tex]\[ \text{Hypotenuse} = \text{Leg length} \times \sqrt{2} \][/tex]
Substituting the length of the leg into the formula:
[tex]\[ \text{Hypotenuse} = 12 \, \text{cm} \times \sqrt{2} \][/tex]
Thus, the length of the hypotenuse is:
[tex]\[ 12 \sqrt{2} \, \text{cm} \][/tex]
Among the given options, the correct one is:
[tex]\[ 12 \sqrt{2} \, \text{cm} \][/tex]
This is approximately equal to 16.970562748477143 cm. However, we recognize that [tex]\(12 \sqrt{2} \, \text{cm}\)[/tex] is the exact value and should be chosen as the answer:
[tex]\[ \boxed{12 \sqrt{2} \, \text{cm}} \][/tex]
