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)

Question

Responses

2 cm
2 cm

22–√ cm
2 Start Root 2 End Root cm

42–√ cm
4 Start Root 2 End Root cm

23–√ cm

Answer 1

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 find the length of the leg as follows:

\[ \text{Leg} = \frac{4}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm} \]

Therefore, the length of the leg is \(2\sqrt{2}\) cm.

The correct response is:

2√2 cm