Question

The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of itsâ height, and inversely as the length of the beam. A beam feetâ long, with a width of inches and a height of inches can support a maximum load of pounds. If a similar board has a width of inches and a height of âinches, how long must it be to support âpounds?

Answer 1

The question is incomplete.Here is the complete question.

The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?

Answer: It must be 392 inches or approximately 33 feet.

Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of proportionality, i.e., if divided, the result is a constant.

For the first load:

width = 6in

height = 4in

length = 13ft or 156in

weight = 800lbs

Then, constant will be:

$\frac{6.4^{2}}{156} k = 800$

$k=\frac{800.156}{96}$

k = 1300

For the similar beam:

$\frac{8.7^{2}}{L}1300=1300$

L = 49.8

L = 392in or 32.8ft

A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.