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
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.
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.