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Presuming the rug covers the patio this is solved using simultaneous equations, with the two variables being the Length (L) and the Width (W)

The first equation is the area: L x W = 36

The second is the relationship between the area and the length: W = L + 5

Thus solving these gives W = 4 feet & L = 9 feet

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Q: The area of a rug is 36 square feet the length of patio is 5 feet longer than width what is the width of the rug?
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