Question 743087
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 {{{ (20+2b)(30+2b) = 1200 }}}

Multiplying this out gives {{{ 600 + 20x2b + 30x2b + 4b^2 = 600 }}}

Subtracting 600 from both sides and simplifying gives:
{{{ 4b^2 + 100b -600 = 0  }}}

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,