Question

Madisyn is planting crops in a triangular garden. The triangular garden can be

seen below. What is the amount of fencing that Madisyn needs?

Answer 1

The amount of fencing Madisyn needs is approximately 20.77 m

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;

`Distance \ between \ points \ given \ the \ coordinates = \sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

Therefore, the length of AB is
`\sqrt{\left (5-6 \right )^(2)+\left (6-0 \right )^(2)} = √(37)`

The length of BC is
`\sqrt{\left (5-(-1) \right )^(2)+\left (6-5 \right )^(2)} = √(37)`

The length of AC is
`\sqrt{\left (6-(-1) \right )^(2)+\left (0-5 \right )^(2)} = √(74)`

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.