Arectangle is twice as long as it is wide. if its length is increased by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 cm2. find the dimensions of the original rectangle.

Original Rectangle:
 long: L = 2W
 Width: W
 New rectangle:
 long: L = 2W + 4
 Width: W - 3
 Area: 100
 We have then:
 A = (2W + 4) * (W-3)
 Rewriting:
 A = 2W ^ 2 - 6W + 4W - 12
 A = 2W ^ 2 - 2W - 12
 Substituting the area:
 2W ^ 2 - 2W - 12 = 100
 Rewriting:
 2W ^ 2 - 2W - 112 = 0
 Which roots are:
 W = -7
 W = 8
 Taking the positive root, we look for the dimension of the original triangle:
 L = 2W = 2 (8) = 16
 
 The dimensions of the original rectangle are:
 W = 8 cm
 L = 16 cm

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