Find the perimeter of the triangle.

Question

hosentak · Accepted Answer

The perimeter of a triangle is the sum of its side lengths so we first need to find the three side lengths of the triangle.
Since the side from (−3,−1) to (2,−1) is a horizontal segment, we can count the number of units between the two points to find its length. Since 2−(−3)=5, then the length of this side is 5.
Since the side from (2,−1) to (2,3) is a vertical segment, we can count the number of units between the two points to find its length. Since 3−(−1)=4, then the length of this side is 4.
The side between from (-3,-1) to (2,3) is not a horizontal or vertical segment so we need to use the distance formula $d = \sqrt{{(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2}}$ to find the lenght of this side:
$d = \sqrt{{(- 3 - 2)}^{2} + {(- 1 - 3)}^{2}}$ Substitute.
$= \sqrt{{(- 5)}^{2} + {(- 4)}^{2}}$ Substract.
$= \sqrt{(25 + 16)}$ Evaluate the powers.
$= \sqrt{41}$ Add.
The length of the third side is then $\sqrt 41 \approx 6.4 .$
The perimeter of the triangle is then about 5+4+6.4=15.4. The exact perimeter is $5 + 4 + \sqrt{41} = 9 + \sqrt{41}$

Find the perimeter of the triangle.[Graph]

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