A ladder is placed on a stairway (as shown). What is the length of the shorter leg?

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**Details and Assumptions**:

- Each step has the same horizontal run of \(15 \text{ cm}\) and vertical run of \(10 \text{ cm}.\)
- Each leg of the ladder rests on the horizontal midpoint of a step.
- The angles that the legs make with the steps are congruent.

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