Question

builders have to follow guidelines on the rise and run of stairs when building a staircase. one acceptable ratio is a rise of 9 3/4inches for a run of 10 3/4inches. if a builder is using this ratio to build a staircase that is 17 feet high, how deep will the staircase need to be? round to the nearest tenth of a foot.

Answer 1

we have that

ratio rise to run is equal to

rise/run=9 3/4/10 3/4

Convert mixed numbers to an improper fraction

so

9 3/4=9+3/4=39/4

10 3/4=10+3/4=43/4

therefore

the ratio is equal to

(39/4)/(43/4)=39/43

Applying proportion

39/43=17/x

solve for x

x=(17*43)/39

x=18.7 ft