Let:
By similarity, we have:
Can you proceed from here?
Find the length of the longest rod which can be carried horizontally around a corner from a corridor 8m wide into one 4m wide. (Without involving angles if possible)
VIEW the attachment for the figure.
Hello, Kaloda!
This is a classic problem . . .
Find the length of the longest rod which can be carried horizontally around a corner
from a corridor 8m wide into one 4m wide.
Let be the length of the rod.Code:| | A * | | * | y| * | | * | P D + - - - * - - - - - - - - | 4 : * | : * 8| 8: * | : * | : * * - - - + - - - - - * - - - - C 4 E x B
. . Then: . .[1]
We see that
. . Hence: .
Substitute into [1], set , and solve for maximum
I get (substituting for y into the square of the length) the following as the critical value:
I began with:
Implicitly differentiating with respect to , we have:
Since we must have , to find the extrema, we may equate:
Multiplying through by and distributing, we find:
Factor:
Discarding the negative root, we have:
I suspect you have set it up like Soroban did, so your critical value may be different from what I have.