Question 1169508: Help me solve this, please!
The length of a rectangle is one more than the width. If the dimensions are both decreased by 2 units, the ares of the new rectangle is 30 sq. units less than the area of the original rectangle. Find the area of the original rectangle.
Answer by ikleyn(52884)   (Show Source):
You can put this solution on YOUR website! .
Let x be the width of the original rectangle.
Then its length is (x+1), according to the condition,
and the area is x*(x+1).
The decreased dimensions are (x-2) and ((x+1)-2) = (x-1),
so the decreased area is (x-2)*(x-1).
From the condition,
(x-2)*(x-1) = x*(x+1) - 30.
Simplify
x^2 - 3x + 2 = x^2 + x - 30
30 + 2 = x + 3x
32 = 4x
x = 32/4 = 8.
ANSWER. The original dimensions are 8 units (the width) and 8+1 = 9 units (the length).
Solved.
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