Atelier Ryza: Ever Darkness & the Secret Hideout

If her legs are $95 \text{ cm}$ long, which is smaller than the length from her navel to the bottom of her feet, and the ratio of the length from her navel to the bottom of her feet and the length from the top of her head to her navel is $\phi$ , then the length from the top of her head to her navel must be greater than $\frac{95}{\phi}$ , so that her whole height $h$ is $h > \frac{95}{\phi} + 95 = 95\phi$ or $h > 153 \text{ cm}$ .

If the length from the top of her head to her bottom of her neck is $24 \text{ cm}$ long, which is greater than the length from the top of her head to her throat, and the ratio of the length from her throat to her navel and the length from the top of her head to her throat is $\phi$ , then the length from her throat to her navel must be smaller than $24\phi$ , which makes the length from the top of her head to her navel smaller than $24\phi + 24$ , and since the ratio of the length from her navel to the bottom of her feet and the length from the top of her head to her navel is also $\phi$ , then the length from her navel to the bottom of her feet is smaller than $(24\phi + 24)\phi$ , so that her whole height $h$ is $h < (24\phi + 24)\phi + (24\phi + 24) = 24(\phi + 1)^2$ or $h < 165 \text{ cm}$ .

Therefore, $153 \text{ cm} < h < 165 \text{ cm}$ , and the only choice that fits this criteria is $\boxed{161 \text{ cm}}$ .