Question

question 23 of 25

in a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg?

a. \\(1 : \sqrt{2}\\)
b. \\(2 : 1\\)
c. \\(\sqrt{2} : 1\\)
d. \\(1 : 1\\)

Explanation:

Identify the properties of the triangle

Using the 45-45-90 Triangle Theorem knowledge point

$$ \text{Angles} = 45^\circ, 45^\circ, 90^\circ $$

$$ \text{Leg}_1 = x, \quad \text{Leg}_2 = x $$

Calculate the ratio of the legs

Using the 45-45-90 Triangle Theorem knowledge point

$$ \text{Ratio} = \frac{\text{Leg}_1}{\text{Leg}_2} = \frac{x}{x} = \frac{1}{1} = 1:1 $$

Answer:

• A. \(1:\sqrt{2}\)
• B. \(2:1\)
• C. \(\sqrt{2}:1\)
• D. \(1:1\) (Correct answer)