The length of a rug is 6 ft more than the width. the area is 40^2 ft. find the length and width of the rug.

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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