SOLUTION: A rectangle is twice as long as it is wide. If its length and width are each reduced by 1 inch, the area of the rectangle is reduced by 14 square inches. Find the dimensions of the

Algebra ->  Surface-area -> SOLUTION: A rectangle is twice as long as it is wide. If its length and width are each reduced by 1 inch, the area of the rectangle is reduced by 14 square inches. Find the dimensions of the      Log On


   

Question 371646: A rectangle is twice as long as it is wide. If its length and width are each reduced by 1 inch, the area of the rectangle is reduced by 14 square inches. Find the dimensions of the original rectangle.
Answer by amoresroy(361) About Me  (Show Source):
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A rectangle is twice as long as it is wide. If its length and width are each reduced by 1 inch, the area of the rectangle is reduced by 14 square inches. Find the dimensions of the original rectangle.
Let x = the width of the rectangle
2x = the length of the rectangle
(x-1)(2x-1) = x(2x) - 14
Solve for x
2x^2-x-2x+1 = 2x^2 -14
Combine like terms
-3x = -15
x = 5
2x = 10
The dimensions of the original rectabngle are
width = 5 inches
length= 10 inches