The load that can be supported by a rectangular beam there is jointly as the width of the beam in the square of its height and inversely as the length of the beam a been 14 feet long with the width of 4 inches and the height of 6 inches can support a maximum load of 800 pounds if a similar board has a width of 9 inches and the height of 5 inches how long must be to support 1400 pounds

12.5 feet

Step-by-step explanation:

The description of the load-carrying capacity of the beam translates as ...

load = k·w·h²/l

Filling in the numbers, we can find the constant k:

800 lb = k· (4 in) (6 in) ² / (14 ft)

k = (800·14 lb·ft) / (144 in³) = 700/9 lb·ft/in³

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Then the length to support 1400 lb with the other given dimensions will be ...

1400 lb = (700/9) lb·ft/in³ * (9 in) (5 in) ²/l

l = 700·25/1400 ft = 12.5 ft

The beam must be at most 12.5 ft long to support 1400 pounds.