Question

Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 4 inches wide, 3 inches high, and 18 feet long can support a maximum of 3 tons. What is the maximum weight that could be supported by a beam that is 7 inches wide, 4 inches high, and 6 feet long?

Answer 1

Uing f for weight (force), we have
f = kwh^2/l
So,

fl/(wh^2) is constant

You need f such that

6f/(7*4^2) = (3*18)/(4*3^2)
f = 28 tons

Answer 2

The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/3 foot​ wide, 1/3 foot​ high, and 16 feet long can support 30 ​tons, find how much a similar beam can support if the beam is 3/4 foot​ wide, 1/2 foot​ high, and 20 feet long