Sure, let's solve this step by step.
A 45-45-90 triangle is a special type of isosceles right triangle where the two non-hypotenuse sides, or legs, are congruent. This means that these two legs have the same length. Let's denote the length of each leg as [tex]\( x \)[/tex].
Now, since both legs are of equal length, the ratio of one leg to the other leg is calculated as follows:
1. Identify the lengths of the legs:
Both legs are equal, so we have two segments of length [tex]\( x \)[/tex].
2. Set up the ratio:
The ratio of the length of one leg to the length of the other leg is:
[tex]\[
\frac{x}{x}
\][/tex]
3. Simplify the ratio:
Simplifying [tex]\( \frac{x}{x} \)[/tex]:
[tex]\[
\frac{x}{x} = 1
\][/tex]
Thus, the ratio of the length of one leg to the length of the other leg in a 45-45-90 triangle is:
[tex]\[
1:1
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{1:1} \)[/tex], which corresponds to option B.
