Area: A chemical plant is rectangular and has a length of

[learnerjack]

A chemical plant is rectangular and has a length of 120 meters and a width of 50 meters. A safety zone of uniform width surrounds the plant. If the area of the safety zone equals the area of the plant, what is the width of the safety zone?

 

[Deleted member 4993]

Re: Area problem

A chemical plant is rectangular and has a length of 120 meters and a width of 50 meters. A safety zone of uniform width surrounds the plant. If the area of the safety zone equals the area of the plant, what is the width of the safety zone?

Draw a sketch first:

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|   x   _____________   x    |
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|       |            |       |       
|       |            |       |
|       |            |       |
|       |            |       |
|       |            |       |
|       |            |       |
|   x   | ___________|   x   | 
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|____________________________|

Now name the unknown

Let the width of the safety zone = x

What is the area of the plant?

What is the area of (plant + safety zone)?

What is the area of the safety zone?

and continue....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[winsome]

Re: Area problem

Let the width of the safety zone = x
Area of a rectangle = length * width
Area of plant = 120 * 50 = 6000 m[sup:134hq1cf]2[/sup:134hq1cf]
Area of Safety zone + Area of plant = (120 + 2x) * (50 +2x)
Area of Safety zone = (120 + 2x) * (50 + 2x) – 6000
Area of Safety zone = 6000 + 240x + 100x + 4x[sup:134hq1cf]2[/sup:134hq1cf] – 6000
Area of Safety zone = 4x[sup:134hq1cf]2[/sup:134hq1cf] + 340x
As area of the safety zone equals the area of the plant, so
4x[sup:134hq1cf]2[/sup:134hq1cf] + 340x = 6000
Divide both sides by 4
x[sup:134hq1cf]2[/sup:134hq1cf] + 85x = 1500
x[sup:134hq1cf]2[/sup:134hq1cf] + 85x -1500 = 0
x[sup:134hq1cf]2[/sup:134hq1cf] + 100x -15x – 1500 = 0
(x -15)(x + 100) = 0
So x = 15 or x = -100
As safety zone width can’t be negative, so x = 15.
Answer: Width of safety zone is 15m.
ads deleted

 

[Denis]

Re: Area problem

Nice sneaky way to advertize, winsome.
Btw, doing all the work for a student usually doesn't help the student. :shock:

 

[mmm4444bot]

learnerjack and winsome are the same person.

Winsome is just wasting volunteers' time here, again.