The perimeter of the water wheel [tex]8\sqrt{10}[/tex]
The correct option is (A)
The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. To derive the formula, let us consider two points in 2D plane A( x, a) and B(y, b).
So, the distance between two points be: [tex]\sqrt{(y-x)^{2}+(b-a)^{2}}[/tex]
As water wheel is designed in the shape of regular octagon.
To find the perimeter of the water wheel.
Since the water wheel is in the shape of regular octagon all sides are equal.
Using Distance Formula,
D= [tex]\sqrt{(4-3)^{2}+(0-3)^{2}}[/tex]
= [tex]\sqrt{10}[/tex]
So, the side of regular octagon will be [tex]\sqrt{10}[/tex].
Perimeter of Regular Octagon = 8 x side
= [tex]8\sqrt{10}[/tex]
Hence, the perimeter of the water wheel [tex]8\sqrt{10}[/tex]
Learn more about Distance Formula here:
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