Exercise 20 Page 410

P ≈ 16.97 units.

Practice makes perfect

To find the perimeter of rectangle BCEF, we will add together the lengths of its sides, EF, FB, BC, and CE. Using the Distance Formula, we can calculate the lengths of each of these sides. Let's start with EF.

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

SubstitutePoints

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

EF = sqrt(( - 2- 2)^2 + ( 1-( - 3))^2)

SubNeg

a-(- b)=a+b

EF=sqrt((- 2-2)^2+(1+3)^2)

AddSubTerms

Add and subtract terms

EF=sqrt((- 4)^2+4^2)

CalcPow

Calculate power

EF=sqrt(16+16)

AddTerms

Add terms

EF=sqrt(32)

The lengths of all 4 sides can be calculated in the same way.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
EF	(2,-3) (-2,1)	sqrt(( -2- 2)^2+( 1-( -3))^2)	sqrt(32)
FB	(-2,1) (0,3)	sqrt(( 0-( -2))^2+( 3- 1)^2)	sqrt(8)
BC	(0,3) (4,-1)	sqrt(( 4- 0)^2+( -1- 3)^2)	sqrt(32)
CE	(4,-1) (2,-3)	sqrt(( 2- 4)^2+( -3-( -1))^2)	sqrt(8)

By calculating the sum of the lengths of all 4 sides, we can find the perimeter of the rectangle.

P=EF+ FB + BC + CE

SubstituteValues

Substitute values

P= sqrt(32)+sqrt(8)+sqrt(32)+sqrt(8)

UseCalc

Use a calculator

P = 16.97056...

RoundDec

Round to 2 decimal place(s)

P≈ 16.97

The rectangle's perimeter is P ≈ 16.97 units.

Hints

Check the answer

Practice exercises

Assess your skill