Answer:
Each side of the fountain is 5 units
Step-by-step explanation:
Given:
All the sides of the vertices are equal.
Vertices of the fountain
(7.5,5),
(11.5,2),
(7.5,−1),
(2.5,−1),
(−1.5,2),
(2.5,5)
To Find:
Length of the each side of the fountain = ?
Solution:
Let us find the Length of the hexagon using the distance formula
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_2)^2}[/tex]
Now lets find the length of AB
Length of AB = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_2)^2}[/tex]
where
[tex]x_1[/tex] = 7.5
[tex]x_2[/tex] = 11.5
[tex]y_1[/tex] = 5
[tex]y_2[/tex] = 2
Substituting the values we get,
Length of AB = [tex]\sqrt{(11.5 - 7.5)^2 +(5-2)^2}[/tex]
Length of AB = [tex]\sqrt{(4)^2 +(3)^2}[/tex]
Length of AB = [tex]\sqrt{16 +9}[/tex]
Length of AB = [tex]\sqrt{25}[/tex]
Length of AB = 5
Since all the sides of the hexagon are said to be equal, the length of the sides of the hexagon is 5 units
