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.

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 6 inches wide, 2 inches high, and 12 feet long can support a maximum of 14 tons. What is the maximum weight that could be supported by a beam that is 4 inches wide, 3 inches high, and 14

feet long?

Answer 1

W = k * w * h^2/ L

14 = k * 6 * 2^2 / 12

14 = k * 24/12

14 = 2 * k

k = 7

So w = 7 * 4 * 3^2 / 14

= 28 * 9 / 14

= 18 tons