# 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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