Gabriellaeid
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- Oct 27, 2021
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Would love if someone could help me solve the following. Given the data in the drawing inserted below I need to find the minimal length of the ladder 
Max and Min questions
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Harry_the_cat
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You ultimately want to minimise length of ladder (L), so you'll need to find an expression for L in terms of one variable.
Start by letting the unknown length along the bottom be x and the height up the wall be h.
Use similar triangles to get h in terms of x.
Then you should be able to get an expression for L (or L^2) in terms of x only.
See what you can do with that and then get back to us.
Start by letting the unknown length along the bottom be x and the height up the wall be h.
Use similar triangles to get h in terms of x.
Then you should be able to get an expression for L (or L^2) in terms of x only.
See what you can do with that and then get back to us.
Dr.Peterson
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- Nov 12, 2017
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I tried this several ways, and always found myself having to solve a quartic equation, so I thought I was stuck.
I finally realized it can be solved if you recognize a negative value of x that produces a minimum (and therefore a solution of that quartic), then use division to obtain a simple cubic you can solve. The result agrees with what I found using GeoGebra.
Where does this problem come from? It isn't exactly easy ... nor is it just an algebra problem, as I needed calculus.
I finally realized it can be solved if you recognize a negative value of x that produces a minimum (and therefore a solution of that quartic), then use division to obtain a simple cubic you can solve. The result agrees with what I found using GeoGebra.
Where does this problem come from? It isn't exactly easy ... nor is it just an algebra problem, as I needed calculus.