The load that a beam of fixed length can support varies jointly as its width and the square of its depth. A beam 40 cm wide and 20 cm deep can support a load of 880kg. How much can a beam 50 cm wide and 10 cm deep support?

Question

anonymous · Answer

Two changes.  Consider them one at a time.  

If we make the beam wider, it will make it stronger in a linear relationship, so the new beam is 5/4 as strong as the original.

If we make the depth half as much, the beam will be weaker as the square, so the beam will be only (1/2)^2=1/4 as strong as the original.

Apply both changes by multiplication, so the new beam is about 5/16 as strong as the original.  Since the original could support 880kg, the new one should be able to support about 275 kg.

anonymous · Answer

I get it :) thanks for the help!

anonymous · Answer

No sweat.  Do math every day.