Try this solution (see the attachmed pictures), modify the design according to the local requirements.
Note, the points (-6;-16) and (-9;-28) are the intersection points of the parabola and the line, given in the condition.
Consider the functions below. f(x) = x² - 6x - 27 g(x) = x - 9
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The formula for finding the area of a rug: 
Plugging in the values we know, we can solve for s.
Take the square root of both sides.
is approximately equal to 8.89
So, 8.89 feet is the answer.
Plugging in the values we know, we can solve for s.
Take the square root of both sides.
So, 8.89 feet is the answer.