Find the perimeter of the triangle.[Graph]

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 ${\displaystyle d=\sqrt{{(x2-x1)}^2+{(y2-y1)}^2}}$ to find the lenght of this side: 
${\displaystyle d=\sqrt{{(-3-2)}^2+{(-1-3)}^2}}$  Substitute. 
${\displaystyle =\sqrt{{(-5)}^2+{(-4)}^2}}$  Substract. 
${\displaystyle =\sqrt{(25+16)}}$  Evaluate the powers. 
${\displaystyle =\sqrt{41}}$  Add. 
The length of the third side is then ${\displaystyle \surd 41\approx 6.4.}$ 
The perimeter of the triangle is then about 5+4+6.4=15.4. The exact perimeter is ${\displaystyle 5+4+\sqrt{41}=9+\sqrt{41}}$