To solve this problem, we can set up an inverse variation equation:
W = k/L
where W represents the weight supported by the beam, L represents the length of the beam, and k is the constant of variation.
Given that a 5m beam can support 1400kg, we can substitute these values into the equation:
1400 = k/5
To find the value of k, we can solve for it:
k = 1400 * 5
k = 7000
Now we can use this value of k to determine how many kilograms a 13m beam can support:
W = 7000/13
W ≈ 538.46 kg
Therefore, a 13m beam can support approximately 538.46 kilograms.