Question 919311: a square filed with side 30 meter is inside by a path of uniform width. If the area of the path is 256 meter square, the width of the path is
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a square filed with side 30 meter is inside by a path of uniform width.
If the area of the path is 256 meter square, the width of the path is
:
If I understand this right, this is a square field, 30m on a side, with a path of uniform width around the outside of it.
:
let x = the width of the path
The overall dimensions of the area which includes the path:
(2x+30 by (2x+30)
:
overall area - field area = path area (256 sq/m)
(2x+30)*(2x+30) - 30*30 = 256
FOIL
4x^2 + 60x + 60x + 900 - 900 = 256
4x^2 + 120x = 256
A quadratic equation
4x^2 + 120x - 256 = 0
simplify, divide by 4
x^2 + 30x - 64 = 0
Factors to
(x + 32)(x - 2) = 0
the positive solution
x = 2 m is the width of the path
:
:
See if that works out, the overall dimensions will be 34 by 34
34*34 = 1156, overall area
30*30 = 900, field area
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difference 256, path area
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