Question 992320

let the length of the room be {{{L}}} and the width {{{W}}}
if a rectangular room is {{{4.15m}}} longer than it is wide,we have 

{{{L=W+4.15m}}}.....eq.1

and if its perimeter {{{P=2(L+W)}}} is {{{27.9m}}} we have

{{{2(L+W)=27.9m}}}......eq.2....substitute {{{W+4.15m}}} for {{{L}}}

 {{{2(W+4.15m+W)=27.9m}}}...solve for {{{W}}}

 {{{(W+4.15m+W)=27.9m/2}}}


 {{{(W+4.15m+W)=13.95m}}}

{{{2W=13.95m-4.15m}}}

{{{2W=9.8m}}}

{{{W=9.8m/2}}}

{{{highlight(W=4.9m)}}}

go back to eq.1, substitute {{{4.9m}}} for {{{W}}} and solve for {{{L}}}

{{{L=W+4.15m}}}.....eq.1

{{{L=4.9m+4.15m}}}

{{{highlight(L=9.05m)}}}

so, the dimensions of the room are {{{highlight(L=9.05m)}}} and {{{highlight(W=4.9m)}}}