In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg?A.1:1B.1:C.2:1D.:1SUBMITarrow_backPREVIOUS

1. Break Down the Problem

In a 45-45-90 right triangle, both legs are equal in length. We need to determine the ratio of the lengths of the two legs.

2. Relevant Concepts

In a 45-45-90 triangle, the following properties hold:

• The two legs (let's call them $a$ and $b$) are equal: $a = b$.
• The ratio of the legs is thus $\frac{a}{b}$.

3. Analysis and Detail

Since both legs are equal, the ratio can be expressed as: $\frac{a}{b} = \frac{a}{a} = 1$ Thus, the ratio of the lengths of one leg to the other leg in a 45-45-90 triangle is 1:1.

4. Verify and Summarize

The properties of a 45-45-90 triangle confirm that both legs are indeed equal. Thus, our calculation is consistent with the definition of the triangle.

Final Answer

The ratio of the length of one leg to the length of the other leg is 1:1 (Option A).