The strength of a rectangular wooden beam varies directly with the square of the depth of its cross section. If a beam with a depth of 3.5 inches can support 1000 pounds, how much weight can the same type of beam hold if it's depth is 12 inches?

The beam with depth of 12 inches can hold 11755 poundsStep-by-step explanation:Let strength be sand depth be dThen according to given statement "The strength of a rectangular wooden beam varies directly with the square of the depth of its cross section."s∝d²When the proportionality symbol is removed, a proportionality constant is introducedSo,[tex]s=kd^2\\As\ we\ know\\d = 3.5\\s= 1000\\1000= k(3.5)^2\\1000=k*12.25\\k=\frac{1000}{12.25}\\k=81.633\\Now\ putting\ d=12\\s=81.633 * (12)^2\\s=81.633*144\\s=11755.152\\Rounding\ off\ to\ nearest\ pound\\s=11755\ pounds[/tex]The beam with depth of 12 inches can hold 11755 poundsKeywords: Proportion, Direct variationLearn more about variation at:brainly.com/question/2115122brainly.com/question/2116906#LearnwithBrainly