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

23–√ cm
2 Start Root 3 End Root cm

42–√ cm

Answer 1

In a 45-45-90 triangle, the sides have a specific relationship:

- The lengths of the legs are equal.
- The length of the hypotenuse is \( x\sqrt{2} \), where \( x \) is the length of each leg.

Given that the hypotenuse is 4 cm, we can set up the equation:

\[
x\sqrt{2} = 4
\]

To find \( x \), we divide both sides by \( \sqrt{2} \):

\[
x = \frac{4}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2}
\]

Thus, the length of each leg is:

\[
2\sqrt{2} \text{ cm}
\]

Therefore, the correct response is:

**2√2 cm**