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
2 cm
2 cm
4–√2 cm
4 Start Root 2 End Root cm
2–√3 cm
2 Start Root 3 End Root cm
2–√2 cm
Responses
2 cm
2 cm
4–√2 cm
4 Start Root 2 End Root cm
2–√3 cm
2 Start Root 3 End Root cm
2–√2 cm
Answers
GPT-4o mini
In a 45-45-90 triangle, the relationship between the legs and the hypotenuse is given by:
- The lengths of the legs are equal, and each leg is \(\frac{\text{hypotenuse}}{\sqrt{2}}\).
Given that the hypotenuse is 4 cm, the length of each leg is:
\[
\text{Leg} = \frac{4}{\sqrt{2}} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of each leg is \(2\sqrt{2}\) cm.
So the correct response is \(2\sqrt{2} \text{ cm}\).
- The lengths of the legs are equal, and each leg is \(\frac{\text{hypotenuse}}{\sqrt{2}}\).
Given that the hypotenuse is 4 cm, the length of each leg is:
\[
\text{Leg} = \frac{4}{\sqrt{2}} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of each leg is \(2\sqrt{2}\) cm.
So the correct response is \(2\sqrt{2} \text{ cm}\).