Question

Use the distance formula to find the perimeter of the triangle below. Round you answer to the nearest hundredth. ​

Answer 1

jAlright, let's take this problem step-by-step:

What is the perimeter:

 ⇒ all the side-lengths added up

    ⇒ need to find side-length using distance formula

                $Distance_._. Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

                         - (x₁,y₁): first point

                         - (x₂,y₂): second point

Let's solve:

• Find length of AC

           ⇒ first point: (5,7)

           ⇒ second point: (3,3)

           $Distance =\sqrt{(3-5)^2+(3-7)^2} =\sqrt{4+16} =\sqrt{20} =4.472$

• Find length of AB

          ⇒ first point: (5,7)

          ⇒ second point:(8,6)

           $Distance=\sqrt{(8-5)^2+(6-7)^2} =\sqrt{9+1} =\sqrt{10}=3.162$

• Find length of BC

          ⇒ first point: (8,6)

          ⇒ second point: (3,3)

           $Distance = \sqrt{(3-8)^2+(3-6)^2} =\sqrt{25+9} =\sqrt{34}=5.831$

Now let's solve for the perimeter:

  $Perimeter = 4.472+ 3.126+ 5.831=13.429$

Answer: 13.43 (rounded to the nearest hundredth)

Hope that helps!

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