# 4.2: Variables on Both Sides

**At Grade**Created by: CK-12

*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

- 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
10 units longer than the perimeter of the square, which of the following equations are true?

a.

b.

c.

d. none of these

- What value of
x 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:**

Use o for the equals sign.

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

An equilateral triangle has sides of length

- 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

- If each side of the hexagon is of length
2x , 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

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

## Problem 5 – Regular Decagon and 15-gon

The side lengths of the regular decagon and

- Find the difference in their perimeters.

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