SOLUTION: A rectangualr garden measuring 8 m by 20 m has its area increased by 60 m^2 by the addition of a walk of uniform width around all sides. What is the width of the walk?

Question 84734: A rectangualr garden measuring 8 m by 20 m has its area increased by 60 m^2 by the addition of a walk of uniform width around all sides. What is the width of the walk?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular garden measuring 8 m by 20 m has its area increased by 60 m^2 by the addition of a walk of uniform width around all sides. What is the width of the walk?
:
Think of it this way.
:
Let x = width of the path:
Total dimension = (2x+8) by (2x+20)
:
Total area (including the garden & the walkway) - area of the garden = 60 sq/m
:
[(2x+8)(2x+20)] - (8 * 20) = 60
:
(4x^2 + 56x + 160) - 160 = 60
:
4x^2 + 56x + 160 - 160 - 60 = 0
:
4x^2 + 56x - 60 = 0
;
Simplify, divide equation by 4:
x^2 + 14x - 15 = 0
:
factors easily:
(x + 15)(x - 1) = 0
x = +1 ft is the width of the walkway (other solution would not make sense)
:
Check solution of x = 1, Dimensions of the total area: (2+8)*(2+20)
10 * 22 = 220
8 * 20 = 160
--------------
differ = 60 sq/ft

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