Question

A standard interior staircase has steps each with a rise (height) of 21 cm and a run (horizontal depth) of 24 cm. Research suggests that the stairs would be safer for descent if the run were, instead, 29 cm. For a particular staircase of total height 5.04 m, how much farther would the staircase extend into the room at the foot of the stairs if this change in run were made?

Answer 1

Answer:

The staircase would extends 1.20 m if the changes were made.

Step-by-step explanation:

Acording tho the statement the total heigth is 5.04 m, that is 504 cm, each steps rises 21 cm. with this information we can calculte how many steps are in the whole staircase:

$Number steps= \frac{Total heigth}{each step} \\Number steps= \frac{504}{21} = 24 steps$

To calculate how much the staircase will extend, whe have to multiply the horizontal depth times the number of steps.

using the run of 24 cm that gives us a lengt of 576 cm and if the changes were made the new length will be 696 cm.

So the staircase would extend an amount of (696 - 576), that is 120 cm, or 1.20 m, if the changes were made.