SOLUTION: A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border?

Question 170089This question is from textbook
: A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border? This question is from textbook

Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border?
-------------------
Draw the picture of the garden with its border.
Original area of the garden = 80 sq. ft.
-------------
Let the width of the border be "x".
-------------
New area = (8+2x)(10+2x) = 80 +143
80 + 36x + 4x^2 = 80 + 143
4x^2 + 36x - 143 = 0
x = [-36 +- sqrt(36^2 - 4*4*-143]/8
x = [-36 +- sqrt(3584)]/8
x = [-36 +- 59.87]/8
Positive solution:
x = 2.98 ft. (width of the border)
========================================
Cheers,
Stan H.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border?
-----------------
It's exactly 3 feet. 11 x 13 = 143
--------------
New area = (8+2x)(10+2x) = 143
80 + 36x + 4x^2 = 143
4x^2 + 36x - 63 = 0
x = [-36 +- sqrt(36^2 - 4*4*-63]/8
x = [-36 +- sqrt(2304)]/8
x = [-36 +- 48]/8
Positive solution:
x = 1.5 ft. (width of the border)
1.5 ft on all sides increases the width and length by 3 feet.
---------------------
The other solver seems to have read it as "increases it by 143", and his solution is correct for that.

RELATED QUESTIONS
A small garden measures 6 ft by 10 ft. A uniform border around the garden increases the... (answered by josgarithmetic,ikleyn)
a rectangular garden 10 feet wide and 12 feet long is surrounded by a rock border of... (answered by checkley77)
A landscape architect designed a decorative grass border around a large community garden. (answered by scott8148)
A small rectangular playground that is 10 feet by 14 feet is going to have a grass border (answered by checkley77)
Hello I have been trying to figure out this word problem and not sure why I keep getting... (answered by solver91311,josgarithmetic)
Lee has a rectangular plot to use for a flower garden. She plans to include a gravel... (answered by Theo)
Any help with the following word problem would be great. I just really need the help... (answered by Earlsdon)
A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, (answered by ankor@dixie-net.com)
A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, (answered by mananth,dharvin1965@yahoo.com)