SOLUTION: A garden is in the shape of a rectangle, 20 metres by 8 metres. Around the outside is a border of uniform width and in the middle is a square pond. The width of the border is the

Algebra ->  Algebra  -> Surface-area -> SOLUTION: A garden is in the shape of a rectangle, 20 metres by 8 metres. Around the outside is a border of uniform width and in the middle is a square pond. The width of the border is the      Log On

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Question 170130: A garden is in the shape of a rectangle, 20 metres by 8 metres. Around the outside is a border of uniform width and in the middle is a square pond. The width of the border is the same as the width of the pond. The size of the area, which is not occupied by either border or pond, is 124m^2. Find the width of the border.
Answer by ankor@dixie-net.com(12695) About Me  (Show Source):
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A garden is in the shape of a rectangle, 20 meters by 8 meters. Around the
outside is a border of uniform width and in the middle is a square pond.
The width of the border is the same as the width of the pond. The size of the
area, which is not occupied by either border or pond, is 124m^2.
Find the width of the border.
:
Let x = the width of the border and also the width of the pond
Then
x^2 = area of the pond
and
(20*8) - x^2 = (160-x^2) = area of the garden (minus the pond)
therefore:
160 - x^2 = 124
-x^2 = 124 - 160
-x^2 = -36
x^2 = 36
x = sqrt%2836%29
x = 6 meters is the width of the border
:
:
Check solution
20 by 8 area - pond area =
160 - 6^2 =
160 - 36 = 124