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The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides are m2 – 2m + 1 and 2m2 + 3m + 5. What is the third side?
- a)3m2 – 5m + 3
- b)3m2 + 5m – 4
- c)5m2 – 3m + 5
- d)5m2 – 3m + 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides...
Third side = 6m2 – 4m + 9 – (m2 – 2m + 1 + 2m2 + 3m + 5)
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The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides...
Third side = 6m2 – 4m + 9 – (m2 – 2m + 1 + 2m2 + 3m + 5)
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The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides...
Perimeter of the Triangle:
The perimeter of the triangle is given as 6m² - 4m + 9.
Given Sides:
Two sides of the triangle are m² - 2m + 1 and 2m² + 3m + 5.
Finding the Third Side:
To find the third side, we need to subtract the sum of the given sides from the perimeter of the triangle.
Calculations:
Given sides: (m² - 2m + 1) + (2m² + 3m + 5) = 3m² + m + 6
Perimeter of the triangle: 6m² - 4m + 9
Subtracting:
Perimeter - Sum of given sides = 6m² - 4m + 9 - (3m² + m + 6) = 3m² - 5m + 3
Therefore, the third side of the triangle is 3m² - 5m + 3, which corresponds to option 'A'.
The perimeter of the triangle is given as 6m² - 4m + 9.
Given Sides:
Two sides of the triangle are m² - 2m + 1 and 2m² + 3m + 5.
Finding the Third Side:
To find the third side, we need to subtract the sum of the given sides from the perimeter of the triangle.
Calculations:
Given sides: (m² - 2m + 1) + (2m² + 3m + 5) = 3m² + m + 6
Perimeter of the triangle: 6m² - 4m + 9
Subtracting:
Perimeter - Sum of given sides = 6m² - 4m + 9 - (3m² + m + 6) = 3m² - 5m + 3
Therefore, the third side of the triangle is 3m² - 5m + 3, which corresponds to option 'A'.
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