SOLUTION: A building is constructed over a circular pond. The ratio from the longest side of the rectangular building is 4:3 and the perimeter is 280 units. The edge of the pond is 4 units

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Question 169792: A building is constructed over a circular pond. The ratio from the longest side of the rectangular building is 4:3 and the perimeter is 280 units. The edge of the pond is 4 units beyond each corner of the building on the diagonal when viewed in an aerial photo. The building owners plan to put water plants in the area of the pond that will recieve sunlight at noon. The plants caost $1.25 each and require a surface area of 30 square units to be healty when mature. What is the total cost of the plants neede to cover the available area?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A building is constructed over a circular pond.
The ratio from the longest side of the rectangular building is 4:3 and the perimeter is 280 units.
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4x+3x = 280
7x = 280
x = 40
length = 3x = 120 units
width = 4x = 160 units
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diagonal = sqrt[120^2+160^2] = 200 units
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Area = 120*160 = 19200 sq. units
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The edge of the pond is 4 units beyond each corner of the building on the diagonal when viewed in an aerial photo.
diameter of the pond = 200 +2*4 = 208 units
area of the pond = 104^2(pi) = 10816pi sq. units
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The building owners plan to put water plants in the area of the pond that will recieve sunlight at noon.
That area = pond area - rectangle area = 10816pi - 19200 = 14779.47 sq. units
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The plants cost $1.25 each and require a surface area of 30 square units to be healthy when mature. What is the total cost of the plants needed to cover the available area?
cost = [14779.47/30]*1.25 = 492.65*1.25 = $615.81
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Cheers,
Stan H.