 # Find the perimeter of the triangle.[Graph] abondantQ 2021-03-05 Answered

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