# Math

One side of a rectangle is 20 cm larger than the other side. If you make the smaller side two times larger and the larger side three times larger, then the perimeter of the new rectangle would be 240 cm. Find the lengths of the sides of the original rectangle.

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1. If the original sides were x and y, they have told you that
y = x+20
the new perimeter is
2(2x + 3y) = 2(2x+3(x+20)) = 2(2x+3x+60) = 2(5x+60) = 10x+120 = 240
so, x=12, making y=32

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2. Initially:
Width = W.
Length = W+20 cm.

Increased side:
Width = 2W.
Length = 3W+60 cm.
P = 2(2W) + 2(3W+60) = 240 cm.
W = 12 cm.
Width = 2W = 24 cm.
Length = 3W + 60 = 36 + 60 = 96 cm.

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3. Original Rectangle: Length = 12+20 = 32 cm, Width = 12cm.

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