Beginning Algebra, 11th Edition

Step 3 Write an equation.Use the formula for the perimeter of a triangle.

Perimeter of a triangle Substitute.

Step 4 Solve. Combine like terms.

Subtract 4. Divide by 3.

Step 5 State the answer.The shortest side, s, has length 4 ft. Then

, Length of medium side

and Length of longest side

Step 6 Check.The medium side, 5 ft, is 1 ft longer than the shortest side, and the

longest side, 7 ft, is 3 ft longer than the shortest side. Futhermore, the

perimeter is ft, as required. NOW TRY

Finding the Height of a Triangular Sail

The area of a triangular sail of a sailboat is

(Recall that “ ” means “square feet.”) The base of the

sail is 12 ft. Find the height of the sail.

Step 1 Read the problem. We must find the height of

the triangular sail.

Step 2 Assign a variable.Let the height of the

sail, in feet. See FIGURE 11.

Step 3 Write an equation.The formula for the area of

a triangle is where is the area, bis

the base, and his the height.

Area of a triangle

Step 4 Solve. Multiply.

Divide by 6.

Step 5 State the answer.The height of the sail is 21 ft.

Step 6 Checkto see that the values and satisfy the

formula for the area of a triangle. NOW TRY

OBJECTIVE 3 Solve problems involving vertical angles and straight angles.

FIGURE 12shows two intersecting lines forming angles that are numbered ➀, ➁, ➂,

and ➃. Angles ➀and ➂lie “opposite” each other. They are called vertical angles.

Another pair of vertical angles is ➁and ➃. Vertical angles have equal measures.

Now look at angles ➀and ➁. When their measures are added, we get 180°, the

measure of a straight angle. There are three other such pairs of angles: ➁and ➂,

➂and ➃, and ➀and ➃.

a =126, b= 12, h= 21

21 =h

126 = 6 h

126 = a=126, b= 12

1

2

1122 h

a=

1

2

bh

a = a

1

2 bh,

h=

ft^2

126 ft^2.

EXAMPLE 4

4 + 5 + 7 = 16

s + 3 = 4 + 3 = 7 ft.

s + 1 = 4 + 1 = 5 ft

4 =s

12 = 3 s

16 = 3 s+ 4

16 =s + 1 s+ 12 + 1 s+ 32

P=a+b+c

122 CHAPTER 2 Linear Equations and Inequalities in One Variable

NOW TRY
EXERCISE 4
The area of a triangle is
77. The base is 14 cm.
Find the height of the
triangle.

cm^2

12 ft

h

FIGURE 11

2

4

1 3

FIGURE 12

NOW TRY ANSWERS

5 ft, 12 ft, 13 ft 4.11 cm

NOW TRY
EXERCISE 3
The perimeter of a triangle is
30 ft. The longest side is 1 ft
longer than the medium side,
and the shortest side is 7 ft
shorter than the medium side.
What are the lengths of the
three sides?

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