Beginning Algebra, 11th Edition

SECTION 2.5 Formulas and Additional Applications from Geometry^125

Solving for a Specified Variable

Solve for B.

Multiply by 2 to clear the fraction.

Distributive property

Subtract hb.

Combine like terms.

Divide by h.

or B=

2 a -hb

h

2 a- hb

h

= B,

2 a- hb

h

=

hB

h

2 a-hb= hB

2 a-hb= hb+hB- hb

2 a= hb+hB

2 a= h 1 b+ B 2 2 # 21 = 22 = 1

2 a= 2 #

1

2

h 1 b+ B 2

a=

1

2

h 1 b+ B 2

a=^12 h 1 b+ B 2

NOW TRY EXAMPLE 9

EXERCISE 9

Solve
for a.

S=^12 1 a+b+c 2

NOW TRY

NOTE The result in Example 9can be written in a different form as follows:

a-b

c =

a

c-

b

B= c

2 a-hb

h

=

2 a

h

-

hb

h

=

2 a

h

NOW TRY ANSWER -b.

9. a= 2 S-b-c

Complete solution available
on the Video Resources on DVD

2.5 EXERCISES

1.In your own words, explain what is meant by each term.

(a)Perimeter of a plane geometric figure

(b)Area of a plane geometric figure

2.Concept Check In parts (a)– (c), choose one of the following words to make the state-

ment true: linear, square, or cubic.

(a)If the dimensions of a plane geometric figure are given in feet, then the areais given

in feet.

(b)If the dimensions of a rectangle are given in yards, then the perimeteris given in

yards.

(c) If the dimensions of a pyramid are given in meters, then the volumeis given in

meters.

3.Concept Check The measure of a straight angle is. Vertical angles

have measures.

(the same/different)

4.Concept Check If a formula has exactly five variables, how many values would you

need to be given in order to find the value of any one variable?

Our goal

is to isolate B.

Multiplying 2 times

here is notan

application of the

distributive property.

1

2