The strength of a rectangular beam varies directly as the square of it depth. If the strength
of a beam 10 inches deep is 3600 pounds per
square inch, what is the strength of a beam four
six inches deep?

For a beam with rectangular shape (width ‘b’, height ‘h’), the section modulus which decides the strength is expressed as:

W = b*h^2/6

At the same time:

b^2 + h^2 = 60^2

From the above equations:

W = b*(60^2 - b^2)/6 = (-b^3/6 + 3600*b/6)

The value of ‘W’ is maximum when dW/db = 0

dW/db = d/db( (-b^3/6 + 3600*b/6)) = -b^2/2 + 600 =0

From the above: b = sqrt(1200) = 34.64 cm,

and h = sqrt(3600 - b^2) = 49.00 cm

(Check sqrt (34.64^2 + 49^2) = 60.01 cm = D)

Step-by-step explanation:

Direct variation equation:

In this case it is:

Substitute the given values and solve for k:

The equation becomes:

Now, find the value of y, when x is 6:

Note, I took the depth as 6 inches but the question is a bit confusing by saying "four six inches". If it is 4 inches then your answer will be: