QUADRATIC EQUATION GEOMETRY PROBLEM
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QUADRATIC EQUATION GEOMETRY PROBLEM

[From: ] [author: ] [Date: 12-04-17] [Hit: ]
the lawn goes uniformly (x) around the building...make a diagram.........
a rectangular building 100m by 80m is to be surrounded by a lawn of uniform width. The area of the lawn must be equation to the area of the building. FInd the with of the lawn to the nearest tenth of a meter?

You're either suppose to use factoring or quadratic formula to solve.


please explain the solution step by step and accurately


thanks

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the area of the building (the footprint of the base) is 100 * 80 = 8000 m^2

the area of the lawn = area of the building = 8000 m^2

the lawn goes uniformly (x) around the building...make a diagram...

the dimensions of the building AND the lawn are: (100 + 2x) by (80 + 2x)

the area of the building plus the lawn - area of building = area of lawn

(100 + 2x)(80 + 2x) - 8000 = 8000

expand and solve for x:

8000 + 360x + 4x^2 - 16000 = 0

4x^2 + 360x - 8000 = 0

x^2 + 90x - 2000 = 0

use the quadratic formula...

x = [- 90 ± √(16100)]/2 = [- 45 ± 5√161]

get out your calculator...make a contribution...the negative answer is extraneous.

id est

[x ≈ 18.44 m]

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If the width of the lawn is x, then the outside perimeter of the lawn will be (100 + 2x) by (80 + 2x). The area of lawn thus will be (100+2x)(80+2x) - (100)(80), this last term being the area of the building in the middle. This expression must then equal the area of the building. So multiplying out we get
100*80 + 200x + 160x + 4*x^2 - 8000 = 8000. This simplifies to 4*x^2 + 360x - 8000 = 0, and then down to x^2 + 90x - 2000 = 0. Using the quadratic formula we take the positive solution 18.4 m.

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The area of the building is 80 times 100 square metres = 8000 square metres.
So the area of the lawn is 8000 square metres = the area of the space less the area of the building

The space is rectangular so the width has to be(80 + 2x)* (100 + 2x) - 8000 = 8000
==> (80 +2x)(100+2x) = 16000
==> 8000 + 160x + 200x + 4x^2 = 16000
==> x^2 + 90x + 2000 = 4000 (divide everything in the last line by 4)
==> x^2 + 90x - 2000 = 0
==> x =( -90 +/- sqrt(90^2 + 8000))/2
==> x = (-90 +/- 126.886)/2
==> x = 18.44 or some negative number, which can be ignored
So, width of the lawn (to nearest 10th of a meter) is 18.4 meters.
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keywords: EQUATION,PROBLEM,QUADRATIC,GEOMETRY,QUADRATIC EQUATION GEOMETRY PROBLEM
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