SOLUTION: A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm exponent 2. Find the original length of the rectangle.

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Question 176311: A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm exponent 2. Find the original length of the rectangle.
Answer by MathTherapy(10555) About Me  (Show Source):
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A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm exponent 2. Find the original length of the rectangle.
width = w length = 2w

Original area = 2w^2

(w - 2)(2w - 2) + 68 = 2w^2
2w^2 - 6w + 4 + 68 = 2w^2
- 6w = - 72
w = 12

Original length = 24 cm