Question 168149
lets call the length of the blue mat y and the width of the border x, which means the side of the entire area is y+2x

we also know that, y=(3/4)(y+2x)--->y=(3/4)y+(6/4)x--->1/4y=6/4x-->y=6x

since area of the red(28)  is equal to entire area minus the blue area

we have {{{(y+2x)^2-(y)^2=28}}}

{{{y^2+4xy+4x^2-y^2=28}}}--->{{{4x^2+4xy=28}}}

substitute value of y which is 6x into the equation

{{{4x^2+4(x)(6x)=28}}}---->{{{28x^2=28}}} {{{x^2=1}}}
{{{x=1}}}

y=6x(1)=6

so the sides of the entire area is y+2x --->{{{highlight(6+2=8)}}} meters