Question

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?

Answer 1

The beam with depth of 12 inches can hold 11755 pounds

Step-by-step explanation:

Let strength be s

and

depth be d

Then according to given statement "The strength of a rectangular wooden beam varies directly with the square of the depth of its cross section."

s∝d²

When the proportionality symbol is removed, a proportionality constant is introduced

So,

$s=kd^2\\As\ we\ know\\d = 3.5\\s= 1000\\1000= k(3.5)^2\\1000=k*12.25\\k=\frac{1000}{12.25}\\k=81.633\\Now\ putting\ d=12\\s=81.633 * (12)^2\\s=81.633*144\\s=11755.152\\Rounding\ off\ to\ nearest\ pound\\s=11755\ pounds$

The beam with depth of 12 inches can hold 11755 pounds

Keywords: Proportion, Direct variation

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