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?

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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?
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Draw the picture of the garden with its border.
Original area of the garden = 80 sq. ft.
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Let the width of the border be "x".
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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)
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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?
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It's exactly 3 feet. 11 x 13 = 143
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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.
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The other solver seems to have read it as "increases it by 143", and his solution is correct for that.