Question 712636
A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path?
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Let x = width (m) of path
then
area of "path+garden" = (2x+3)(2x+4)
area of "garden" = 3*4 = 12
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From:"The area of the garden and path is 6 times as great as the area of the garden." we get our equation:
(2x+3)(2x+4) = 6*12
4x^2+8x+6x+12 = 72
4x^2+14x+12 = 72
4x^2+14x-60 = 0
2x^2+7x-30 = 0
rewrite middle term:
2x^2+12x-5x-30 = 0
group:
(2x^2+12x)-(5x+30) = 0
2x(x+6)- 5(x+6) = 0
(x+6)(2x-5) = 0
x = {-6, 5/2}
we can throw out the negative solution (extraneous) leaving:
x = 5/2
or
x = 2.5 m