i need help with this and how you work out the equation

Question

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length. If a beam that is

6

inches​ wide,

6

inches​ deep, and

3

feet long can support a weight of

576

​pounds, how much weight could the same type of beam that is

6

inches​ wide,

4

inches​ deep, and

12

feet long​ support?

Answer 1

s=kwsqrd/L

where k = constant of proportionality

w=width, d=depth, L=Length, s=strength

substitute w=6, d=6, L=3, s=576

and solve for k

576=k(6)(sqr6)/3

96=ksqr6/3

48=ksqr6/6

48 =k/sqr6

k = 48sqr6

s =48wsqr(6d)/L

plug in w=6,d=4,L=12

s=48(6)sqr(6x4)/12=24sqr24

=48sqr6 lbs

= about 117.576 lbs

strength= about 118 pounds if width=6,depth=4, Length=12

strength=576 lbs if width =6, depth=6 and Length =3

major difference is L=12 makes the Length 4 times as Long

so strength will be roughly 1/4 as large