Three identical rectangular prisms, each with a square base of side length $s$ cm and a height of $h$ cm, are arranged in a line and glued together along their square bases. The total surface area of the resulting prism is $\frac{10}{7}$ times the surface area of one original prism. Which of the following is the ratio of the height to the side length of the base, $\frac{h}{s}$?