Math problem question

Question

The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its​ height, and inversely as the length of the beam. A beam 13 feet​ long, with a width of 4 inches and a height of 6 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 1

L = kWH^2/L

800=k4(6)^2/13

k= 800(13)/4(36) = 50(13)/9 =650/9

k = 650/9= 72 2/9

W=8, H=7, L=1300

1300=(650/9)8(7)^2/L

L = (650/9)(8)(49)/1300

L =21 7/9 inches long to support 1300 lbs.