Can you check my answer for this Pythagorean theorem problem?

[IlovePi]

Hello and good morning (or night)! I was wondering if I solved this problem correctly and I would greatly appreciate some feedback!

This is the problem:

And this is my work(please excuse my blurry chromebook photo):


So, did I solve this question correctly and if not, what did I miss? Thank you for taking your time to read this and I hope you have a nice day!

 

[Dr.Peterson]

Hello and good morning (or night)! I was wondering if I solved this problem correctly and I would greatly appreciate some feedback!

This is the problem:
View attachment 25556
And this is my work(please excuse my blurry chromebook photo):
View attachment 25559

So, did I solve this question correctly and if not, what did I miss? Thank you for taking your time to read this and I hope you have a nice day!

The only thing I'd do differently is to give a decimal answer, since no one is going to go to the store and ask for \(16\sqrt{109}\) meters of wire! And therefore the simplification is unnecessary. Unless, of course, you were explicitly told to give an "exact" answer (which would not be genuinely exact, as it would exclude extra needed for attachment at the ends).