SOLUTION: I understand how to find the area of a border, but, my difficulty is in the word problems when the exact dimensions are not given such as: A rectange is 3x as long as it is wide.

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Question 58860This question is from textbook Algebra Structur and Method Book 1
: I understand how to find the area of a border, but, my difficulty is in the word problems when the exact dimensions are not given such as: A rectange is 3x as long as it is wide. If its length and width are both decreased by 2cm, its area is decreased by 36cm2. find its original dimensions.
This question is from textbook Algebra Structur and Method Book 1

Answer by stanbon(57377) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle is 3x as long as it is wide. If its length and width are both decreased by 2cm, its area is decreased by 36cm2. find its original dimensions.
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To understand word problems you normally have to draw the picture.
Draw a rectangle inside another rectangle.
The dimensions of the outer rectangle are 3x and x
It's area is 3x^2
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The dimensions of the inner rectangle are (3x-2) and (x-2)
The smaller area is (3x-2)(x-2)=3x^2-8x+4
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EQUATION:
larger area - smaller area = 36
3x^2-(3x^2-8x+4)= 36
8x-4=36
8x=40
x=5 cm
3x=15 cm
These are the original dimensions.
Cheers,
Stan H.