Question

is the perimeter of δxyz? your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Identify coordinates

From the graph, coordinates are: \( X(1, 8) \), \( Y(10, 0) \), \( Z(5, -5) \).

Step2: Calculate \( XY \)

Using distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \):
\( XY = \sqrt{(10 - 1)^2 + (0 - 8)^2} = \sqrt{81 + 64} = \sqrt{145} \approx 12.0 \)

Step3: Calculate \( YZ \)

\( YZ = \sqrt{(5 - 10)^2 + (-5 - 0)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.1 \)

Step4: Calculate \( XZ \)

\( XZ = \sqrt{(5 - 1)^2 + (-5 - 8)^2} = \sqrt{16 + 169} = \sqrt{185} \approx 13.6 \)

Step5: Sum lengths for perimeter

Perimeter \( = XY + YZ + XZ \approx 12.0 + 7.1 + 13.6 = 32.7 \)

Answer:

32.7