SOLUTION: A garden plot 4m by 12m has one side along a fence as shown below. A border of uniform width(x) is to be dug along three of the sides. The area of the garden and border is 96 sq. m

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Question 275034: A garden plot 4m by 12m has one side along a fence as shown below. A border of uniform width(x) is to be dug along three of the sides. The area of the garden and border is 96 sq. m. What is the width of the border?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A garden plot 4m by 12m has one side along a fence as shown below.
A border of uniform width(x) is to be dug along three of the sides.
The area of the garden and border is 96 sq. m.
What is the width of the border?
:
Let x = the width of the uniform border
then for a 3 sided border:
overall dimensions: (x + 4) by (2x + 12
:
over all area:
(x+4)*(2x+12) = 96
FOIL
2x^2 + 12x + 8x + 48 = 96
:
2x^2 + 20x + 48 - 96 = 0
:
2x^2 + 20x - 48 = 0
Simplify divide by 2:
x^2 + 10x - 24 = 0
Factor
(x+12)(x-2) = 0
Positive solution
x = 2 meters is the width of the 3 sided border
;
:
Check solution
that makes the overall dimensions 6 by 16;
6 * 16 = 96 sq/m is the overall area