Designing a staircase

A standard interior staircase has steps each with a rise (height) of 19 cm 19 \text{ cm} and a run (horizontal depth) of 23 cm. 23 \text{ cm}.

Research suggests that the stairs would be safer for descent if the run were, instead, 28 cm. 28 \text{ cm}. For a particular staircase of total height 4.56 m, 4.56 \text{ m}, how much farther into the room would the staircase extend if this change horizontal depth were made?

Note: Assume the same number of horizontal as vertical parts to the steps.

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