Let's make "x" be the width of the patio.
Then the length of the patio would be 4*x.
And the perimeter of the patio would be the sum of all four sides, or x+(4*x)+x+(4*x)=100 feet.
This simplifies to 10x=100 feet.
And the width of the patio x=<<10=10>>10 feet.
And the length of the patio is 4*x = 4*10 = 40 feet.
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