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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

7. Using Congruent Triangles

Finish the assignment

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Exercise 25 Page 638

Use the Distance Formula.

about 17.5 units

Practice makes perfect

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)

a-(- b)=a+b

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

Add and subtract terms

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

Calculate power

JK=sqrt(9+4)

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)

Use a calculator

P= 17.498760...

Round to 2 decimal place(s)

P≈ 17.5

The triangle's perimeter is approximately 17.5 units.

Subchapter links

Communicate Your Answer p.633

Monitoring Progress p.634-635