Question

find n.
8√2 mm
45°
45°
n
write your answer in simplest radical form.
blank millimeters

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the legs are congruent. Each leg is $8\sqrt{2}$ mm.

Step2: Apply Pythagorean theorem

The hypotenuse $n$ is calculated as:
$$n = \sqrt{(8\sqrt{2})^2 + (8\sqrt{2})^2}$$

Step3: Simplify the squares

$$(8\sqrt{2})^2 = 8^2 \times (\sqrt{2})^2 = 64 \times 2 = 128$$

Step4: Sum the squared legs

$$n = \sqrt{128 + 128} = \sqrt{256}$$

Step5: Simplify the square root

$$\sqrt{256} = 16$$

Answer:

16 millimeters