Question 1068948
Assuming possible right triangle shape for the flag,
"width" w
"length" 4w
{{{(w(4w))/2=72}}}


Rectangular mat,
dimensions y and y+14
{{{y(y+14)=72}}}



Flag:  width 6, length24



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For the mat,
{{{y^2+14y=72}}}
{{{y^2+14y-72=0}}}
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discriminant is {{{22^2}}};


{{{y=(-14+22)/2}}}


{{{y=4}}}


The Mat:  
Dimensions are 4 and 18.