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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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