Basic Mathematics for College Students

Since a rectangle has two lengths and two widths , its perimeter is given by

lwlw, or. 2 l 2 w

l w P

778 Chapter 9 An Introduction to Geometry

Perimeter of a Rectangle

If a rectangle has length and width , its perimeter is

given by the formula

P 2 l 2 w

l w P

Caution! When finding the perimeter of a polygon, the lengths of the sides

must be expressed in the same units.

w

l

EXAMPLE (^2) Find the perimeter of the rectangle shown on
the right, in inches.
StrategyWe will express the width of the rectangle in inches and
then use the formula to find the perimeter of the
figure.
WHYWe can only add quantities that are measured in the same
units.
SolutionSince 1 foot 12 inches, we can convert 3 feet to inches by multiplying
3 feet by the unit conversion factor.
Multiply by 1:.
Write 3 ft as a fraction. Remove the common units of feet from
the numerator and denominator. The units of inches remain.
Do the multiplication.
The width of the rectangle is 36 inches. We can now substitute 8 for , the length,
and 36 for , the width, in the formula for the perimeter of a rectangle.
This is the formula for the perimeter of a rectangle.
Substitute 8 for l,the length, and 36 for w, the width.
Do the multiplication.
Do the addition.
The perimeter of the rectangle is 88 inches.

 88

 16  72

P2( 8 )2( 36 )

P 2 l 2 w

w

l

36 in.



3 ft

1



12 in.

1 ft

12 in.

3 ft3 ft 1 ft  1

12 in.

1 ft

(^) 1 foot12 in.



P 2 l 2 w

Self Check 2

Find the perimeter of the triangle

shown below, in inches.

Now TryProblem 21

2 ft

14 in. 12 in.

8 in.

3 ft

EXAMPLE (^3) Structural Engineering The truss shown below is made
up of three parts that form an isosceles triangle. If 76 linear feet of lumber were
used to make the truss, how long is the base of the truss?
Self Check 3
The perimeter of an isosceles
triangle is 58 meters. If one of its
sides of equal length is 15 meters
long, how long is its base?
Now TryProblem 25
16
 72
88
3
1
6
 2
72
20 ft
Base