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) } = √(32) = √(16) * √(2) \\ d1 = 4 √(2)`

`d2 = \sqrt{ {(2 - - 3)}^(2) + {( 2 - 7}^(2)) } \\ = \sqrt{ {(2 + 3)}^(2) + {(4}^(2)) } = √(25 + 16) \\ d2 = √(41)`

`d3 = \sqrt{ {(6 - 7)}^(2) + {(6 - - 3}^(2)) } \\ = \sqrt{ {( - 1)}^(2) + {9}^(2) } = √(1 + 81) \\ d3 = √(82)`
Now add the 3 together:

`d1 + d2 + d3 \\ = 4 √(2) + √(41) + √(82) \\ = none \: of \: the \: above`