SOLUTION: the area of a rectangular plot 30 feet long and 20 feet wide will be doubled by creating a border around the plot. what width should the border be to accomplish this?

Question 743087: the area of a rectangular plot 30 feet long and 20 feet wide will be doubled by creating a border around the plot. what width should the border be to accomplish this?
Answer by davethejackal(28) (Show Source): You can put this solution on YOUR website!
Let b = width of the border
Current area of the rectangle = 20 x 30 = 600 sq ft
By adding the border on either side of the rectangle its length will be increased by b on one side and b on the other side and so the length becomes 30+2b.
Similarly the width becomes 20+2b

Area of the rectangle with the border = width x length = (20+2b)(30+2b) [1]
We are told this = twice the original area = twice 600 sq ft = 1200 sq ft
Hence
Multiplying this out gives
Subtracting 600 from both sides and simplifying gives:

Factorising gives (4b-20)(b+30)=0 Hence b=-30 or 5. Since b cannot be negative we take 5.

Checking in [1] gives the area including the borders as (20+2(5))(30+2(5)) = 30 x 40 = 1200 sq ft QED.

The width of the border=5ft,
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