SOLUTION: If the length and width of a rectangle is increased by 1meter then the area of a rectangle is increased by 21meter^2 and if the length and width of a rectangle is decreased by 1ma
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Question 1099203: If the length and width of a rectangle is increased by 1meter then the area of a rectangle is increased by 21meter^2 and if the length and width of a rectangle is decreased by 1mater then we area of a rectangle is decreased by 5meter^2.what is the perimeter of a rectangle?
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If the length and width of a rectangle is increased by 1meter then the area of a rectangle is increased by 21meter^2
(L+1)*(w+1) = Lw + 21
FOIL
Lw + L + w + 1 = Lw + 21
combine like terms
Lw - Lw + L + w = 21 - 1
L + w = 20
Therefore
2L + 2W = 40 cm is the perimeter of rectangle 1
the original rectangle: 10 by 10 which is 100 sq/cm
the increased by 1 cm rectangle 11 by 11 which is 121 sq/cm
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These are two different rectangles
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and if the length and width of a rectangle is decreased by 1 meter then we area of a rectangle is decreased by 5meter^2.
(L-1)*(w-1) = Lw - 5
Lw - L - w + 1 = Lw - 5
Lw - Lw - L - w = - 5 - 1
-L - w = -6
multiply by -1
L + w = 6
therefore
2L + 2w = 12 cm is the perimeter of rectangle 2
Original rectangle 4 by 2 which is 8 sq cm
area of one decreased by 1: 3 by 1 = 3 sq/cm
