Question 120314
Let L=length , W=width



Since one side (say the length) "is 2meters longer than the other" then this means

{{{L=W+2}}}



Now using Pythagoreans theorem, we can set up a relationship between the length, width, and the diagonal:



{{{L^2+W^2=10^2}}}



{{{(W+2)^2+W^2=10^2}}} Plug in {{{L=W+2}}}



{{{W^2+4W+4+W^2=10^2}}} Foil



{{{W^2+4W+4+W^2=100}}} Square 10 to get 100




{{{W^2+4W+4+W^2-100=0}}} Subtract 100 from both sides



{{{2W^2+4W-96=0}}} Combine like terms



{{{2(w+8)(w-6)=0}}} Factor the left side 




Now set each factor equal to zero:

{{{w+8=0}}} or  {{{w-6=0}}} 


{{{w=-8}}} or  {{{w=6}}}    Now solve for w in each case



So our possible answers are 

 {{{w=-8}}} or  {{{w=6}}} 



However, since a negative width doesn't make sense, our only solution is {{{w=6}}} 




So the width is 6 meters. Now let's find the length 


{{{L=W+2}}} Start with the given equation



{{{L=6+2}}} Plug in {{{W=6}}}



{{{L=8}}} Add


So the length is 8 meters