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The perimeter formula of a rhombus with angles is:
- a)P = a + b
- b)P = 2(a + b)
- c)P = 2√(d₁² + d₂²)
- d)P = Sum of all sides
Correct answer is option 'C'. Can you explain this answer?
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The perimeter formula of a rhombus with angles is:a)P = a + bb)P = 2(a...
The perimeter formula of a rhombus with angles is given as P = 2√(d₁² + d₂²), where P represents the perimeter, d₁ and d₂ represent the lengths of the diagonals.
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The perimeter formula of a rhombus with angles is:a)P = a + bb)P = 2(a...
Understanding the Perimeter of a Rhombus
The perimeter of a rhombus can be calculated using various methods and formulas. However, it’s crucial to understand the properties of a rhombus to grasp why option 'C' is correct.
What is a Rhombus?
- A rhombus is a type of quadrilateral where all four sides are of equal length.
- The opposite angles are equal, and the diagonals bisect each other at right angles.
Perimeter Formula Explanation
- The perimeter (P) of any polygon is the sum of the lengths of all its sides.
- For a rhombus, since all sides are equal, if one side is denoted as 'd', then:
- P = 4d
However, option 'C' provides a different approach using the diagonal length.
Using Diagonals to Find Perimeter
- If the diagonals of the rhombus are represented as 'd1' and 'd2', the length of each side (d) can be derived from the Pythagorean theorem.
- The formula becomes:
- d = √(d1²/4 + d2²/4)
- Therefore, the perimeter can be rewritten as:
- P = 4 * √((d1² + d2²) / 4)
- This simplifies to:
- P = 2√(d1² + d2²)
Thus, the representation in option 'C' may be interpreted as:
Final Formula
- P = 2√(d² + d²)
This indicates that the perimeter is related to the lengths of the diagonals, making option 'C' a valid representation for certain contexts.
Understanding these concepts helps solidify the geometry of a rhombus and its perimeter calculation.
The perimeter of a rhombus can be calculated using various methods and formulas. However, it’s crucial to understand the properties of a rhombus to grasp why option 'C' is correct.
What is a Rhombus?
- A rhombus is a type of quadrilateral where all four sides are of equal length.
- The opposite angles are equal, and the diagonals bisect each other at right angles.
Perimeter Formula Explanation
- The perimeter (P) of any polygon is the sum of the lengths of all its sides.
- For a rhombus, since all sides are equal, if one side is denoted as 'd', then:
- P = 4d
However, option 'C' provides a different approach using the diagonal length.
Using Diagonals to Find Perimeter
- If the diagonals of the rhombus are represented as 'd1' and 'd2', the length of each side (d) can be derived from the Pythagorean theorem.
- The formula becomes:
- d = √(d1²/4 + d2²/4)
- Therefore, the perimeter can be rewritten as:
- P = 4 * √((d1² + d2²) / 4)
- This simplifies to:
- P = 2√(d1² + d2²)
Thus, the representation in option 'C' may be interpreted as:
Final Formula
- P = 2√(d² + d²)
This indicates that the perimeter is related to the lengths of the diagonals, making option 'C' a valid representation for certain contexts.
Understanding these concepts helps solidify the geometry of a rhombus and its perimeter calculation.
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The perimeter formula of a rhombus with angles is:a)P = a + bb)P = 2(a + b)c)P = 2√(d² + d²)d)P = Sum of all sidesCorrect answer is option 'C'. Can you explain this answer?
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