Question

what is the length of leg \\(s\\) of the triangle below?

a. 2
b. \\(5\sqrt{2}\\)
c. 1
d. 4.4
e. 5.6
f. 4

Explanation:

Identify the triangle type

Using the Special Right Triangles and 45-45-90 Triangle Theorem knowledge points
The given triangle has angles of \(45^\circ\), \(45^\circ\), and \(90^\circ\), making it a \(45^\circ\)-\(45^\circ\)-\(90^\circ\) special right triangle.

Set up the side length ratio

Using the 45-45-90 Triangle Theorem knowledge point

$$ \text{hypotenuse} = \text{leg} \times \sqrt{2} $$

Solve for the leg length s

Using the 45-45-90 Triangle Theorem knowledge point

$$
LATEXBLOCK0
$$

Answer:

• A. 2
• B. \(5\sqrt{2}\)
• C. 1
• D. 4.4
• E. 5.6
• F. 4 (Correct answer)