Answer :
Final answer:
The strength of a rectangular beam is directly proportional to its width and square of thickness. A 4 inches wide and 3 inches thick beam can support 504 pounds, therefore a construction manager can substitute the 4 by 3 beam in place of the 5 by 2 beam because it can support more weight.
Explanation:
The strength (S) of a rectangular beam is directly proportional to its width (w) and the square of its thickness (t) such that S = kwt^2, where k is the constant of proportionality. Given that a 5-inches wide and 2-inches thick beam supports 280 pounds, we can find k as k = S / (wt^2) which gives k = 280 / (5*2^2) = 14.
For a similar beam that's 4 inches wide and 3 inches thick, we can then find its strength S as S = kwt^2, which yields S = 14 * 4 * 3^2 = 504 pounds. Therefore, the similar beam can support 504 pounds.
Since 504 pounds is greater than 280 pounds, a construction manager could substitute the 4 by 3 beam in place of the 5 by 2. The increase in thickness has a greater impact on the strength of a rectangular beam than a decrease in width given the square relationship.
Learn more about Beam Strength here:
https://brainly.com/question/28523449
#SPJ11
