Defining One Variable in Terms of Another
Some problems contain two or more unknown quantities. To solve such problems, first decide which unknown quantity
the variable will represent. Then express the other unknown quantity or quantities in terms of that variable.
The length of a rectangle is 6 in. more than the width. The perimeter of the rectangle is 24 in. What
is the length of the rectangle?
1. Draw a picture of the rectangle in question.
2. What are the two unknown quantities in this problem?
3. Let’s say you’d like to make the variable w for width. How is the length related to this variable?
4. Let’s say you’d like to make the variable l for length. How is the width related to this variable?
5. What is the formula for perimeter?
6. Choose one of the relationships from number 3 or number 4 and substitute it into the formula for perimeter.
7. Solve for the variable!
8. Awesome…try another one!
The width of a rectangle is 2 cm less than its length. The perimeter of the rectangle is 16 cm. What is the
length of the rectangle?