Where are you stuck?
Did you begin by picking some symbols and writing a formula for the strength?
Because the strength (S) is
proportional to width (w) times depth squared (d^2), we have a case of direct variation (with k as the constant of variation).
S = k ∙ w ∙ d^2
The width and depth of the beam are related to the diameter of the log, by the Pythagorean Theorem.
w^2 + d^2 = 121
Can you solve this equation for d^2, and substitute the result into the formula for S?
You'll then have S in terms of w. Determine the derivative S
'.
The maximum S occurs when S
' equals zero; therefore, write S
'=0 and solve that equation for w. Once you know w, you can find d.
Otherwise, please show us what you've done or ask specific questions, so that we can see where to begin helping you. :cool:
