Question

A standard interior staircase has steps each with a rise (height) of 19 cm and a run (horizontal depth) of 23 cm. Research suggests that the stairs would be safer for descent if the run were, instead, 28 cm. For a particular staircase with a total height of 4.57 m, how much farther into the room would the staircase extend if this change in run were made? Start by making a sketch.

Answer 1

The staircase would extend 1.33 m farther into the room.

Step-by-step explanation:

Please see the attached figure for clarification. In red is the extended distance of the staircase. The small black number were the distances used to calculate the extended distance. In the first step, the staircase extends 5 cm farther into the room, in the second, 10 cm and so on. in the seventh step the stairs extend in total:

(7-3)·5 cm + 28 cm= 20 cm + 28 cm = 48 cm inside the room.

The equation for the distance that the staircase would extend into the room will be:

(n° steps -3) · 5 cm + 28 cm.

So, let´s find the number of steps of the staircase. If the total height is 457 cm and every step is 19 cm high, the number of steps will be:

number of steps = 457 cm / 19 cm = 24 steps

Then, the distance that the staircase would extend into the room would be:

(24-3) · 5 cm + 28 cm = 133 cm or 1.33 m