A fence 8ft tall runs parallel to a tall building at a distance of 4ft from the building. what is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? (optimization problem)

Question

hba · Answer

Can you construct a diag ? @kels

anonymous · Answer

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hba · Answer

The two legs on the ladder triangle is the same as the two legs on the similar, bigger triangle.


So,

$$\frac{ 8 }{ y }=\frac{ x }{ 4+y }$$

Solve for y.

amistre64 · Answer

i wonder if this setup would be the shortest ladder

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anonymous · Answer

still confused as to how to set up the problem to answer it in an optimization format..

amistre64 · Answer

its similar to the ladder around a corner one, that i can never really do correctly for some reason

hba · Answer

we just have to minimize is the Lenght of ladder which we will formulate and rearrange for y and yeah then derivate it.

anonymous · Answer

i know L^2 = x^2 + y^2.. 

L = sqrt ((x+4)^2 + (y^2))

hba · Answer

rearrange for y and put it in the equation then diifrentiate it.

anonymous · Answer

8/y= x/(4+y) 

why is it x / (4+y) versus x / (4+x) ?

amistre64 · Answer

http://archives.math.utk.edu/visual.calculus/3/applications.2/ this has a doable setup; this problem is approached in the same manner as the ladder around a corner one

anonymous · Answer

@kels it is 4 + x not 4 + y

anonymous · Answer

sorry according to your diagram it x - 4