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)
A. 2√ 3cm
B. 2√ 2cm
C. 2 cm
D. 4√ 2cm
A. 2√ 3cm
B. 2√ 2cm
C. 2 cm
D. 4√ 2cm
Answers
GPT-4o mini
In a 45-45-90 triangle, the relationship between the legs and the hypotenuse is defined by the ratios: the legs are equal in length, and each leg is \(\frac{\text{hypotenuse}}{\sqrt{2}}\).
Given that the hypotenuse is 4 cm, we can calculate the length of each leg as follows:
\[
\text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of each leg is \(2\sqrt{2}\) cm.
The correct answer is **B. 2√2 cm**.
Given that the hypotenuse is 4 cm, we can calculate the length of each leg as follows:
\[
\text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \text{ cm}
\]
Therefore, the length of each leg is \(2\sqrt{2}\) cm.
The correct answer is **B. 2√2 cm**.