Question

c = 7 cm; y = 5.5 cm; find ( s_2 ).

Explanation:

Step1: Identify geometric relationship

In a right triangle, the length of the leg is the geometric mean of the hypotenuse and the adjacent segment. The formula is $s_2 = \frac{y \times c}{y}$? No, correct formula: $s_2 = \frac{c \times y}{y}$ is wrong. Correct: For right triangle $JKL$ with right angle at $K$, altitude to hypotenuse creates two similar triangles. So $s_2 = \frac{y \times c}{y}$ no, the correct proportion is $\frac{s_2}{c} = \frac{y}{s_2}$? No, correct: $\frac{s_2}{c} = \frac{y}{s_2}$ is incorrect. The correct proportion from similar triangles $\triangle JKL \sim \triangle KJL$ (wait, $\triangle JKL \sim \triangle LKJ \sim \triangle LJK$? No, right triangle altitude theorem: $s_2 = \frac{y \times c}{y}$ no, the formula is $s_2 = \frac{c \times y}{x}$ no, wait: The hypotenuse $JL = c = 7$ cm, segment $y = 5.5$ cm. The leg $s_2$ satisfies $s_2^2 = y \times c$.

Step2: Substitute values and solve

$$s_2 = \sqrt{y \times c}$$
$$s_2 = \sqrt{5.5 \times 7}$$
$$s_2 = \sqrt{38.5} \approx 6.2 \text{ cm}$$

Answer:

6.2 cm