FIND PERIMTER WITH POLYNOMIALS

Perimeter :

Find sum of all sides will give us perimeter. To add or subtract polynomials, we should know about combining like terms.

Adding and subtracting like terms :

5x2 + 3x2 = 8x2

5x2 - 3x2 = 2x2

Since we have x2 for both terms, we call it as like terms.

Find the perimeter of the shapes given below.

Problem 1 :

Solution : 

Perimeter = Sum of all the sides

= (4x - 8) + (3 – 2x) + (11 + y)

= 4x – 8 + 3 – 2x + 11 + y

= 4x – 2x + y – 8 + 3 + 11

= 2x + y + 6

Problem 2 :

Solution :

Perimeter = Sum of all the sides

= (3a - b) + (3a - b) + (3a - b)

= 3a – b + 3a – b + 3a – b

= 3a + 3a + 3a – b – b – b

= 9a – 3b

Problem 3 :

Solution :

Perimeter = Sum of all the sides

= (2y – 3x - 3) + (9x – 3y + 2) + (12 + 5x + 7y)

= 2y – 3x - 3 + 9x – 3y + 2 + 12 + 5x + 7y

= 2y – 3y + 7y – 3x + 9x + 5x – 3 + 2 + 12

= 6y + 11x + 11

Problem 4 :

Solution :

Perimeter = Sum of all the sides

= (6 + 2a) + (3b – 4a + 5) + (6 + 2a) + (3b – 4a + 5)

= 6 + 2a + 3b – 4a + 5 + 6 + 2a + 3b – 4a + 5

= 2a – 4a + 2a – 4a + 3b + 3b + 6 + 5 + 6 + 5

= -4a + 6b + 22

Problem 5 :

Solution :

Perimeter = Sum of all the sides

= (7 + 3x) + (5x² - 2) + (7 + 3x) + (5x² - 2)

= 7 + 3x + 5x² - 2 + 7 + 3x + 5x² - 2

= 5x² + 5x² + 3x + 3x + 7 + 7 – 2 – 2

= 10x² + 6x + 10

Problem 6 :

Solution :

Perimeter = Sum of all the sides

= (4z + 3) + (4z + 3) + (4z + 3) + (4z + 3)

= 4z + 3 + 4z + 3 + 4z + 3 + 4z + 3

= 4z + 4z + 4z + 4z + 3 + 3 + 3 + 3

= 16z + 12

Problem 7 :

Solution :

Perimeter = Sum of all the sides

= (3x² + 5x + 7) + (6x - 3) + (3x² + 5x + 7) + (6x - 3)

= 3x² + 5x + 7 + 6x - 3 + 3x² + 5x + 7 + 6x – 3

= 3x² + 3x² + 5x + 6x + 5x + 6x + 7 + 7 – 3 – 3

= 6x² + 22x + 8

Problem 8 :

Solution :

Perimeter = Sum of all the sides

= 2a² + 3ab + 4a² + 3b² + 6b² - 5ab

= 2a² + 4a² + 3b² + 6b² + 3ab – 5ab

= 6a² + 9b² - 2ab

Problem 9 :

Solution :

Perimeter = Sum of all the sides

= 7 – 2x + 3x² - 4x + 3x² - 4x + 7 – 2x + 5x² + 7x + 3

= 3x² + 3x² + 5x² - 2x – 4x – 4x – 2x + 7x + 7 + 7 + 3

= 11x² - 5x + 17

Recent Articles

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More