SOLUTION: A rectangle is three times as long as it is wide. If the length is decreased by 2 cm and the width is increased by 3 cm, the new rectangle formed has an area of 42 cm2. What are th

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Question 1131528: A rectangle is three times as long as it is wide. If the length is decreased by 2 cm and the width is increased by 3 cm, the new rectangle formed has an area of 42 cm2. What are the dimensions of the original rectangle?
Answer by ikleyn(52790) About Me  (Show Source):
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The dimensions of the rectangle are x and 3x.


Also, the problem says that

(3x-2)*(x+3) = 42.


2x^2 - 2x + 9x - 6 = 42


2x^2 + 7x - 48 = 0.


Solve the quadratic equation; take the positive root - it will be the width.


Then evaluate the length as 3x.