Find the perimeter of the triangle.

abondantQ
2021-03-05
Answered

Find the perimeter of the triangle.

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hosentak

Answered 2021-03-06
Author has **100** answers

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 $d=\sqrt{{(x2-x1)}^{2}+{(y2-y1)}^{2}}$ 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 $\surd 41\approx 6.4.$

The perimeter of the triangle is then about 5+4+6.4=15.4. The exact perimeter is $5+4+\sqrt{41}=9+\sqrt{41}$

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