Question

find s.
write your answer in simplest radical form.
centimeters

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the legs are equal. The given leg is 4 cm, so the other leg is also 4 cm.

Step2: Apply Pythagorean theorem

Use $c^2 = a^2 + b^2$, where $a=b=4$, $c=s$.
$$s^2 = 4^2 + 4^2$$

Step3: Calculate and simplify

$$s^2 = 16 + 16 = 32$$
$$s = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$$

Answer:

$4\sqrt{2}$ centimeters