Formulas and Equation-Solving

Core Focus on Introductory Algebra

Lesson 3.7

Area of a Triangle: A = bhArea of a Rectangle: A = lwDistance: d = rt

1. Find the area of a rectangle when l = 12 and w = 5.

2. Find the area of a triangle when b = 6 and h = 7.

3. Sue drove 3 hours at 52 miles per hour. How far did she drive?

21

Warm-Up

60 square units

21 square units

156 miles

Formulas and Equation-Solving

Solve formulas for a variety of situations.

Lesson 3.7

Good to Know!Formulas are very useful in calculating quantities such as area, perimeter, interest earned in a bank account, distance and batting average.

Previously, you have evaluated these formulas when you were given values to substitute for the variables. In this lesson, you will be able to work backwards to find a missing value in the equation by using your equation-solving skills.

GEOMETRY FORMULAS TO USE IN THIS LESSON

Working with Equations to Solve for a Missing Value

1. Find the formula that fits the situation given.

2. Substitute all known values for the variables into the formula.

3. Determine if any numbers can be multiplied that are on the same side of the equals sign. If so, multiply those numbers.

4. Solve the equation using inverse operations.

5. Write out the answer in a complete sentence.

The area of a triangle is 36 square units. The base is 8 units long. What is the height of the triangle?

Write the formula.

Substitute values for the variables.

Two numbers need to be multiplied on the 36 = 4hright-hand side of the equation before solving.

Solve the equation using inverse operations. 36 = 4h4 4a

9 = haThe height of the triangle is 9 units.

Example 1

12

Area bh

12

36 (8)h

Good to Know!More useful formulas:

I = prt d = rt B = ha

I = interestp = initial deposit

(“principal”)r = rate (as a decimal)t = time

d = distancer = ratet = time

B = batting averageh = hitsa = ‘at bats’

Kenny deposited $500 in a bank account. After 3 years, Kenny earned $90 interest. Use the simple interest formula to determine the interest rate for this account.

Write the formula. a I = prt

Substitute values for the variables. 90 = 500 r 3Multiply before solving. 90 = 1500 r

Solve the equation using inverse 90 = 1500roperations. 1500 1500 0.06 = rChange the decimal to a percent by 0.06(100) = 6%multiplying by 100.

Kenny earned an interest rate of 6%.

Example 2

I = interestp = initial depositr = rate (as a decimal)t = time

The volume of a rectangular box is 60 cubic inches. The length of the box is 5 inches and the height of the box is 2 inches. Find the width of the box.

Write the formula. Volume = lwh

Substitute values for the variables. 60 = (5)w(2)

Multiply the two numbers on the 60 = 10wright-hand side before solving.

Solve the equation using inverse 60 = 10woperations. 10 10

6 = wThe box has a width of 6 inches.

Example 3

Describe a situation outside of the math classroom when you would need to use one of the formulas from this lesson.

Communication Prompt

1. The height of a triangle is 10 inches. The area of the triangle is 30 square inches. What is the length of the triangle’s base?

2. Jackie has had 50 ‘at bats’ this softball season. She has a batting average of 0.320. How many hits has she had?

3. The Parch family drove 8 hours. They traveled a total of 504 miles. What was their rate of speed?

Exit Problems

6 inches

16 hits

63 miles per hour