Answer:
20 m
Explanation:
You want to know the uniform width of a lawn around a 120 m by 80 m building such that the area of the lawn is equal to the area of the building.
Setup
Let x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:
(120 +2x)(80 +2x) = 2(120·80)
Solution
Dividing by 4 gives a slightly simpler equation.
(60 +x)(40 +x) = 60(80)
2400 +100x +x^2 = 4800 . . . . eliminate parentheses
x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form
(x +120)(x -20) = 0 . . . . . . . factor
Values of x that make the factors zero are ...
x = -120, x = 20
Only the positive solution makes any sense in this context.
The width of the lawn must be 20 m.
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Additional comment
The total area of the plot is ...
total area = (building area) + (lawn area)
When the lawn area is equal to the building area, then we have ...
total area = (building area) + (building area)
total area = 2·(building area)
This is the relation we used in the solution above.