Question

You are planning to plant a triangular garden in your backyard, as shown. You plan to put up a fence around the garden to keep out animals. Find the length of fencing you need to the nearest meter.​

Answer 1

Answer:

24 m

Step-by-step explanation:

The lenght of fencing needed is the sum of all sides the triangular garden represented on the coordinate grid.

The lenght of the triangular garden = 16 - 10 = 6 m

Lenght of the height = 8 - 0 = 8 m

Lenght of the hypotenuse can be calculated using coordinates of the two vertices of the ∆ that forms the hypotenuse lenght and also using the distance formula.

Coordinates of the two vertices = (10, 0) and (16, 8).

$distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$(10, 0) = (x_1, y_1)$

$(16, 8) = (x_2, y_2)$

$d = \sqrt{(16 - 10)^2 + (8 - 0)^2}$

$d = \sqrt{(6)^2 + (8)^2}$

$d = \sqrt{36 + 64} = \sqrt{100}$

$d = 10$

Length of fencing = 6 + 8 + 10 = 24 m