Exercise 25 Page 282

To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has three vertices, so it's a triangle. Let's draw it in a coordinate plane.

Before we can find the sum of the side lengths, we must find the length of each side. We can use the Distance Formula to do this. Let's start with JK.

JK = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( -5,3) & ( -2,1)

JK=sqrt(( -2-( - 5))^2+( 1- 3)^2)

SubNeg

a-(- b)=a+b

JK=sqrt((-2+5)^2+(1-3)^2)

AddSubTerms

Add and subtract terms

JK=sqrt(3^2+(-2)^2)

CalcPow

Calculate power

JK=sqrt(9+4)

AddTerms

Add terms

JK=sqrt(13)

We continue by calculating the length of the other two sides KL and JL.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
KL	( -2,1) ( 3,4)	sqrt(( 3-( -2))^2+( 4- 1)^2)	sqrt(34)
JL	( -5,3) ( 3,4)	sqrt(( 3-( -5))^2+( 4- 3)^2)	sqrt(65)

Now, let's calculate the triangle's perimeter. We do so by adding the three sides.

P=JK+KL+JL

SubstituteValues

Substitute values

P=sqrt(13)+sqrt(34)+sqrt(65)

UseCalc

Use a calculator

P= 17.498760...

RoundDec

Round to 2 decimal place(s)

P≈ 17.5

The triangle's perimeter is approximately 17.5 units.