Designing a staircase

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

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

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