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

23–√ cm
2 Start Root 3 End Root cm

22–√ cm
2 Start Root 2 End Root cm

42–√ cm
4 Start Root 2 End Root cm

2 cm

Answer 1

In a 45-45-90 triangle, the relationship between the lengths of the sides is as follows:

• The legs are congruent (equal in length).
• The length of each leg is \(\frac{\text{hypotenuse}}{\sqrt{2}}\).

Given that the hypotenuse is 4 cm, we can calculate the length of each leg:

\[ \text{Length of leg} = \frac{4 \ \text{cm}}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \ \text{cm} \]

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

The correct response is:

\(2\sqrt{2} \text{ cm}\).