The square root of 20200 in order to get the length of just side [tex]$c$[/tex] is [tex]142 \mathrm{~m}$[/tex].
This problem can be solved by simply using the Pythagorean theorem, as you stated at the beginning of the problem, which is: [tex]$a^{2}+b^{2}=c^{2}$[/tex]
You are given the [tex]$a$[/tex] side and [tex]$b$[/tex] side that are needed for this equation, so it's all a matter of plugging in the information you have:
[tex]110^{2}+90^{2}=c^{2}[/tex]
[tex]&110^{2}=12100 \\[/tex]
[tex]&90^{2}=8100[/tex]
[tex]&12100+8100=c^{2} \\[/tex]
[tex]&20200=c^{2}[/tex]
Now, because the [tex]$c$[/tex] is still squared, you must take the square root of 20200 in order to get the length of just side [tex]$c$[/tex] :
[tex]\sqrt{20200} \approx 142 \mathrm{~m}$[/tex].
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