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A local building code requires that all factories must be surrounded by a lawn. The width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. What must be the width of a lawn surrounding a rectangular that measures 120 m by 80 m?

PLEASE HELP

User Martin Pfeffer
by
2.7k points

1 Answer

20 votes
20 votes

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.

__

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.

User Romski
by
3.0k points
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