Minimum Wire Length Calculation for Square Pattern in 10cm Square

[squenshl]

Homework Statement

A wire pattern is inserted into a $10$cm square by making a horizontal line in the middle of the square (not all the way across and with length $x$) and connecting the ends of this line to the closest two corners. What is the minimum value of $x$?

Homework Equations

The Attempt at a Solution

Let $y$ be the length of the wire from the end of $x$ to the corner of the square. This means the total length of the wire is $l = x+4y$.

I extended the blue line $x$ to create a triangle then I used Pythagoras' to get $y^2 = 25+\frac{(10-x)^2}{4}$.

Do I then throw this (meaning $y$) into $l$ then differentiate with respect to $x$ then solve to get my minimum value for $x$ then $y$ which would give me the minimum length for $l$.

Thanks!

 

[Ray Vickson]

Homework Statement

A wire pattern is inserted into a $10$cm square by making a horizontal line in the middle of the square (not all the way across and with length $x$) and connecting the ends of this line to the closest two corners. What is the minimum value of $x$?

Homework Equations

The Attempt at a Solution

Let $y$ be the length of the wire from the end of $x$ to the corner of the square. This means the total length of the wire is $l = x+4y$.

I extended the blue line $x$ to create a triangle then I used Pythagoras' to get $y^2 = 25+\frac{(10-x)^2}{4}$.

Do I then throw this (meaning $y$) into $l$ then differentiate with respect to $x$ then solve to get my minimum value for $x$ then $y$ which would give me the minimum length for $l$.

Thanks!

If that is what you think you should do, why ask us? Just do it!

The point is that you need to start having confidence in your own methods, and you need to be willing to make a mistake, perhaps spending a lot of time on an erroneous approach, then throwing out the worksheets and starting again. That is how all of the homework helpers learned the subject!

 

[Delta2]

The problem statements seems to be ill at least to me. The problem asks for the minimum value of $x$(which if understand correctly is the length of the segment in the middle of square). What prevents us from taking $x=0$?
The only thing I can make is that you probably meant to say the value of $x$ that minimizes the total length $l$ cause that's what your method calculates.

 

[phinds]

The problem statements seems to be ill at least to me. The problem asks for the minimum value of $x$(which if understand correctly is the length of the segment in the middle of square). What prevents us from taking $x=0$?
The only thing I can make is that you probably meant to say the value of $x$ that minimizes the total length $l$ cause that's what your method calculates.