Question

Find the perimeter of triangle ABC.

Answer 1

The perimeter is the distance around. So you need add the 3 sides, each from the distance formula that I showed you.
$d1 = \sqrt{ {(6 - 2)}^{2} + {(6 - 2}^{2}) } \\ = \sqrt{{4}^{2} + {4}^{2} } = \sqrt{32} = \sqrt{16} \times \sqrt{2} \\ d1 = 4 \sqrt{2}$
$d2 = \sqrt{ {(2 - - 3)}^{2} + {( 2 - 7}^{2}) } \\ = \sqrt{ {(2 + 3)}^{2} + {(4}^{2}) } = \sqrt{25 + 16} \\ d2 = \sqrt{41}$
$d3 = \sqrt{ {(6 - 7)}^{2} + {(6 - - 3}^{2}) } \\ = \sqrt{ {( - 1)}^{2} + {9}^{2} } = \sqrt{1 + 81} \\ d3 = \sqrt{82}$
Now add the 3 together:
$d1 + d2 + d3 \\ = 4 \sqrt{2} + \sqrt{41} + \sqrt{82} \\ = none \: of \: the \: above$