Questions: 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: 1 B. 2: 1 C. √2: 1 D. 1: √2

Solution Steps

In a 45-45-90 right triangle, the two legs are congruent, meaning they have the same length. Therefore, the ratio of the length of one leg to the length of the other leg is 1:1.

In a 45-45-90 right triangle, both legs are of equal length. This is a special type of isosceles right triangle where the angles are \(45^\circ\), \(45^\circ\), and \(90^\circ\).

Since both legs are equal, we can denote the length of one leg as \(x\). Therefore, the length of the other leg is also \(x\). The ratio of the length of one leg to the length of the other leg can be expressed as:

\[ \text{Ratio} = \frac{x}{x} = 1 \]

This simplifies to the ratio \(1:1\).

Final Answer