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August 12th, 2014, 03:03 PM   #1
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Calculate the length of the field.

A rectangular playing field 18m wide. It is surrounded by a path 6m wide such that its area is equal to the area of the path. Calculate the length of the field.

Width of path and field = 18m + 12m = 30m
$\text{Area of one path} \ = 30\times6=180m^2\\\text{Area of second path}=180m^2\\\text{Total area of the two path}=360m^2$
We are told that the area of field is equal to area of path. So how do I get the area of the path and of field respectively so that I can equate them and from there get the lenght of the field?
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August 12th, 2014, 03:17 PM   #2
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I think there is path on all four sides of the field.

Set the length of the field to be x
Create expressions for the area of the field and the area of the field + path.
Use those expressions, together with what you are told about the area of the path to get an equation for x.

I get x a little greater than three times the width.

Last edited by v8archie; August 12th, 2014 at 03:20 PM.
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August 12th, 2014, 07:35 PM   #3
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p = path width (6)
w = width (18)
x = length (?)

area field = area path
wx = 2p(x + 2p) + 2pw ; simplify:
x = 2p(2p + w) / (w - 2p)

Finish it...
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August 14th, 2014, 05:47 PM   #4
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  • Completion
Width of path and field = 18m + 12m = 30m
$\text{Area of one path} \ = 30\times6=180m^2\\\text{Area of second path}=180m^2\\\text{Total area of the two path}=360m^2$
Area of the other two paths = $12Lm^2$
Area of field = $18Lm^2$
$\therefore18L=12L+360\\\longrightarrow\\L=60m$
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