Question

find $f$.
write your answer in simplest radical form.
_____ inches

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the legs are equal. The given leg is 5 in, so the other leg is also 5 in.

Step2: Apply Pythagorean theorem

The hypotenuse $f$ is calculated as:
$$f = \sqrt{5^2 + 5^2}$$

Step3: Simplify the expression

$$f = \sqrt{25 + 25} = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$$

Answer:

$5\sqrt{2}$ inches