# The length of a rectangle is three metre more than its width. if both length and width are decreased by 2 metre and the area is deceased by 18 square metre. find the dimensions of the rectangle

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length = x+3 m

Area = x(x+3) = (x²+3x) m²

If both length and width are reduced by 2 meters

width = x-2 m

length = (x+3) - 2 = x+1 m

Area = (x-2)(x+1) = (x² - x - 2) m²

Decrease in area =(x²+3x) m² - (x² - x - 2) m² = 4x+2 m²

given that decrease is 18m²

So 4x+2 = 18

⇒ 4x = 18-2 = 16

⇒ x = 16/4

⇒ x = 4m (width)

length = x+3 = 4+3 = 7m

Length = 7m, width = 4m