The length and width of the rug are 10 ft and 4 ft respectively.
let
the width of the rug = x
Therefore,
length of the rug = 6 + x
area = 40 ft²
area of a rectangle = lw
where
l = length
w = width
area = x(6 + x)
40 = 6x + x²
x² + 6x - 40 = 0
x² - 4x + 10x - 40 = 0
x(x - 4) + 10(x - 4) = 0
(x - 4)(x + 10)
x = 4 or -10
x cannot be negative
Therefore,
x = 4
width of the rug = 4 ft
length of the rug = 4 + 6 = 10 ft
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