Question 1148928
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<pre>

Let "w" be the width of the border, now unknown.


The exterior dimensions are  6 ft by 8 feet with the area  48 sq.feet.


The interior dimensions are (8-2w) ft by (6-2w) ft with the area (6-2w)*(8-2w) sq.feet.


We are given


    (6-2w)*(8-2w) = {{{(1/2)*48}}} = 24.


It is your basic equation to find "w".


Simplify and solve


    48 - 28w + 4w^2 = 24

    4w^2 - 28w + 24 = 0

     w^2 -  7w + 6w = 0

     (w-1)*(w-6) = 0


Only the root  w = 1 makes sense.


<U>ANSWER</U>.  The width of the border is 1 ft.


<U>CHECK</U>.  (6-2*1)*(8-2*1) = 4*6 = 24 sq.ft, which is half of 48 sq.ft.
</pre>

Solved.


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