Question

The load, L, that a beam can support varies directly with the square
of its vertical thickness, h. A beam that is 5 inches thick can
support a load of 2000 pounds. How much weight can a beam hold
that is 9 inches thick?

Answer 1

Solutions 

L(h) = k x h² The constant, k can be found with given values of the load (2000 pounds) and thickness (5 inches). 2000 = k (5² ) Solve: k = 80. Our equation becomes: L(9) = 80 (9² ) Solve: The load with a 9 inch board will be 6480 pounds

Answer 2

Given,
L ∝ h²
So, L = kh²
(Adding a constant 'k')

Case 1 :
2000 = k × (5)²
k = 2000/25 = 80

Case 2 :
L = kh²
L = 80 × (9)²
L = 80 × 81 = 6480 pounds

So, the board of 9 in. can support 6480 pounds of load.