To determine the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle, let's consider the properties of this type of triangle.
A 45-45-90 triangle has the following characteristics:
- It is an isosceles right triangle, meaning its two legs are equal in length.
- The angles are 45°, 45°, and 90°.
Since the triangle is isosceles, the two legs are of equal length. Let's denote the length of each leg as [tex]\( L \)[/tex]. Therefore, both legs are [tex]\( L \)[/tex] units in length.
The ratio of the length of one leg to the length of the other leg is essentially comparing [tex]\( L \)[/tex] to [tex]\( L \)[/tex].
Mathematically, the ratio is given by:
[tex]\[
\frac{L}{L} = 1
\][/tex]
Since both legs have the same length, their ratio is [tex]\(1:1\)[/tex].
Thus, the correct answer is:
D. [tex]\(1:1\)[/tex]
