# 4.2: Variables on Both Sides

*This activity is intended to supplement Algebra I, Chapter 3, Lesson 4.*

## Problem 1 – A Square and a Rectangle Have Different Perimeters.

A square has sides of length . A rectangle has one side that is twice as long and another that is longer than the sides of the square. Do these expressions reflect the description in the picture to the right?

- Write an algebraic expression for the perimeter of the square to the right.
- Write an algebraic expression for the perimeter of the rectangle to the right.
- If the rectangle has a perimeter that is longer than the perimeter of the square, which of the following equations are true?

a.

b.

c.

d. none of these

- What value of will make the equation true?
- Check your answer using the
**App4Math**application by pressing**APPS**and selecting**App4Math**. If your entered answer is correct, the calculator will display**true**.

**Note:** , etc. can be entered using the alpha keys.

Use o for the equals sign.

## Problem 2 – An Equilateral Triangle and a Square have Different Perimeters.

An equilateral triangle has sides of length . A square has sides that are more than twice that length. The perimeter of the square is more than that of the triangle.

- How long are the sides of each polygon?
- Write an algebraic expression for the perimeter of the square.
- Write an algebraic expression for the perimeter of the triangle.
- Write an equation that shows the relationship if the perimeters of the square and triangle.
- Solve this equation and state the length of each side of the square.
- Check your answer using
**App4Math**.

## Problem 3 – A Regular Hexagon and a Regular Octagon

A regular hexagon has sides of length . A regular octagon has sides that are half as long. The perimeter of the hexagon is longer than that of the octagon.

- If each side of the hexagon is of length , what is the length of each side of the octagon?
- Write an algebraic expression for the perimeter of the hexagon.
- Write an algebraic expression for the perimeter of the octagon.
- Write an equation shows the perimeter of the hexagon and octagon, then find the length of the sides of the hexagon.
- Check your answer using
**App4Math**

## Problem 4 – An Equilateral Triangle and a Rectangle

To the right is figure comprised of an equilateral triangle and a rectangle. The perimeter of the rectangle is more than the perimeter of the triangle.

- Find the length, , of each side of the triangle.

## Problem 5 – Regular Decagon and 15-gon

The side lengths of the regular decagon and gon to the right are equal.

- Find the difference in their perimeters.