Question

The strength of a rectangular beam varies jointly as its width and the square of its depth. If the strength of a beam 12 inches wide by 22 inches deep is 3400 pounds per square inch, what is the strength of a beam 9 inches wide and 18 inches deep?

Answer 1

let strength of beam = s
The strength varies jointly as its width and the square of its depth.
s = kwd^2
where k =constant of proportionality
w=width
d=depth

1)s=3400 pounds
w=12 inches
d=22 inches
k=??

plug values in formula
s = kwd^2
3400=k*12*22*22
k=0.585



2) s=??
w=9 inches
d=18 inches
k=0.585

plug in formula

s = kwd^2
s=0.585*9*18*18
s=1705.86~1706 pounds