Question 1117221: A region of land,50 meter by 40 meter is to cross diagonally by a road 15 meters wide. What is the road`s area?
Answer: 844.8 square meter
I really don`t know the solution. Please explain.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A region of land,50 meter by 40 meter is to cross diagonally by a road 15 meters wide. What is the road`s area?
Answer: 844.8 square meter
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Some info is missing, assumptions are made.
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Assuming the centerline of the road is the diagonal:
Use the rectangle with points (0,0), (0,40), (50,40) and (50,0)
The diagonal line has an equation y = 4x/5 = 0.8x
The length of the diagonal is 10sqrt(41) meters
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Using some trig, the lines parallel to the diagonal and 7.5 meters from it are
y = 0.8x + sqrt(41) and
y = 0.8x - sqrt(41)
The 2 areas above and below the centerline are equal.
--> Area of 1 side = 10sqrt(41)*7.5 - the areas of the 2 triangles formed.
The area of the smaller triangle = 7.5*0.8*7.5/2 = 22.5 sq meters.
The area of the larger triangle = 7.5*1.25*7.5/2 = 35.15625 sq meters.
2 triangles' area = 57.65625 sq meters
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Area of each side = 10sqrt(41)*7.5 - 57.5625 = 422.578 sq meters
Times 2 = 845.156 sq meters
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That's close to the stated area.
IDK how the given answer was derived.
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