Question
Use the relationships in 45-45-90 triangles to solve the following problem. If the hypotenuse of a triangle is 4 cm, what is the length of the leg?(1 point)
Responses
22–√ cm
2 Start Root 2 End Root cm
2 cm
2 cm
42–√ cm
4 Start Root 2 End Root cm
23–√ cm
Responses
22–√ cm
2 Start Root 2 End Root cm
2 cm
2 cm
42–√ cm
4 Start Root 2 End Root cm
23–√ cm
Answers
GPT-4o mini
In a 45-45-90 triangle, the lengths of the legs are equal, and the relationship between the legs and the hypotenuse is given by the formula:
\[ \text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}} \]
Given that the hypotenuse is 4 cm, we can calculate the length of each leg as follows:
\[
\text{leg} = \frac{4 \text{ cm}}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of the leg in the triangle is \(2\sqrt{2}\) cm.
So the correct response is:
**2√2 cm**
\[ \text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}} \]
Given that the hypotenuse is 4 cm, we can calculate the length of each leg as follows:
\[
\text{leg} = \frac{4 \text{ cm}}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of the leg in the triangle is \(2\sqrt{2}\) cm.
So the correct response is:
**2√2 cm**