Question

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Answer 1

P = 19.76 units

Explanation:

1. Finding
`\overrightarrow{AB}` (or
`\overrightarrow{BA}`):

`\overrightarrow{AB}=\overrightarrow{OA}-\overrightarrow{OB}= \left[\big5\atop\big3\right]-\left[\big2\atop-\big5\right]= \left[\big5-\big2\atop\big3-(-\big5)\right]=\left[\big3\atop\big8\right]`

2. Calculating length of
`\overrightarrow{OA}\,,\ \overrightarrow{OB}\ \text{and}\ \overrightarrow{AB}`:

`|\overrightarrow{OA}|=√(5^2+3^2)=√(25+9)=√(34)\approx5.831\\\\ |\overrightarrow{OB}|=√(2^2+(-5)^2)=√(4+25)=√(29)\approx5.385\\\\ |\overrightarrow{AB}|=√(3^2+8^2)=√(9+64)=√(73)\approx8.544`

3. Calculating perimeter:

`P=|\overrightarrow{OA}|+|\overrightarrow{OB}|+|\overrightarrow{AB}|=√(34)+√(29)+√(73)\approx5.831+5.385+8.544=19.76`