Math question help

Question

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length. A beam that is 5 inches wide, 6 inches deep, and 10 feet long can support a weight of 900 pounds. If the same type of beam that is 4 inches wide and 4 inches deep can support 400 pounds, how long is the beam?

Answer 1

s = kwd^2/L

900=k5(6^2)/10

90 =5k(36)

10=5k(4)

2 =4k

k=2/4 = 1/2

s =(1/2)wd^2/L

400 = (1/2)4(4^2)/L

100=8/L

L=8/100=0.08 inches Long beam supports 400 lbs, if 4 inches wide, 4 inches deep