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
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]
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.
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.
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.