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4.2: Variables on Both Sides

Difficulty Level: At Grade Created by: CK-12
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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 x. A rectangle has one side that is twice as long and another that is 3 units 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 10 units longer than the perimeter of the square, which of the following equations are true?

a. 4x+10=2(x+3)+2(2x)

b. 4x10=2(x+3)+2(2x)

c. 4x=(x+3)+2x+10

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: x,y,z, 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 x. A square has sides that are 1 more than twice that length. The perimeter of the square is 19 centimeters 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 x. A regular octagon has sides that are half as long. The perimeter of the hexagon is 20 inches longer than that of the octagon.

  • 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 9 centimeters more than the perimeter of the triangle.

  • 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 15gon to the right are equal.

  • Find the difference in their perimeters.

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Date Created:
Feb 22, 2012
Last Modified:
Oct 31, 2014
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