.
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) = = 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.
ANSWER. The width of the border is 1 ft.
CHECK. (6-2*1)*(8-2*1) = 4*6 = 24 sq.ft, which is half of 48 sq.ft.
Solved.
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To see many other similar solved problems, look into the lesson
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.