width of pavement --- x ft
original plot has area of 342 ft^2
inside part is 18-2x by 19-2x, where x > 9
(18-2x)(19-2x) = 110
342 - 74x + 4x^2 = 110
4x^2 - 74x + 232 = 0
2x^2 - 37x + 116 = 0
(x-4)(2x - 29) = 0
x = 4 or x = 29/2 = 14.5
the pavement should be 4 ft wide
check:
flower bed is 10 by 11 or 110 ft^2
A rectangular plot, 18 ft by 19 ft, is to be used for a garden. It is decided to put a pavement inside the entire border so that 110 square feet of the plot is left for flowers. How wide should the pavement be?
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