Answer:
The amount of fencing Madisyn needs is approximately 20.77 m
Step-by-step explanation:
The coordinates of the vertices of the triangular garden are;
A(0, 6), B(6, 5), and C(5, -1)
The length of the sides of the triangle can be found through the given coordinates and the distance between coordinates formula presented as follows;
[tex]Distance \ between \ points \ given \ the \ coordinates = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, the length of AB is [tex]\sqrt{\left (5-6 \right )^{2}+\left (6-0 \right )^{2}} = \sqrt{37}[/tex]
The length of BC is [tex]\sqrt{\left (5-(-1) \right )^{2}+\left (6-5 \right )^{2}} = \sqrt{37}[/tex]
The length of AC is [tex]\sqrt{\left (6-(-1) \right )^{2}+\left (0-5 \right )^{2}} = \sqrt{74}[/tex]
Therefore;
The amount of fencing Madisyn needs = The length of the sides of the triangular garden
The length of the sides of the triangular garden = The length of AB + The length of BC + The length of AC
The length of the sides of the triangular garden = √37 + √37 + √74 ≈ 20.77 m.
The amount of fencing Madisyn needs ≈ 20.77 m.
