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If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is?
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If area of a circle inscribed in a equilateral triangle is 48pi square...
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The area of the circle inscribed in the equilateral triangle is 48π square units.
Finding the Radius of the Circle
- The area of a circle is given by the formula: Area = πr².
- Setting this equal to the given area, we have: πr² = 48π.
- Dividing both sides by π gives: r² = 48.
- Thus, the radius r = √48 = 4√3 units.
Relating Radius to the Side of the Triangle
- For an equilateral triangle, the radius (r) of the inscribed circle is related to the side length (s) by the formula: r = (s√3) / 6.
- Substituting the value of r we found: 4√3 = (s√3) / 6.
Solving for the Side Length
- Cross-multiplying gives: 4√3 * 6 = s√3.
- This simplifies to: s = 24 units.
Calculating the Perimeter of the Triangle
- The perimeter (P) of an equilateral triangle is given by: P = 3s.
- Substituting the side length: P = 3 * 24 = 72 units.
Conclusion
- The perimeter of the equilateral triangle is 72 units.
This detailed breakdown provides clarity on the relationship between the inscribed circle and the equilateral triangle, leading to the final answer.
The area of the circle inscribed in the equilateral triangle is 48π square units.
Finding the Radius of the Circle
- The area of a circle is given by the formula: Area = πr².
- Setting this equal to the given area, we have: πr² = 48π.
- Dividing both sides by π gives: r² = 48.
- Thus, the radius r = √48 = 4√3 units.
Relating Radius to the Side of the Triangle
- For an equilateral triangle, the radius (r) of the inscribed circle is related to the side length (s) by the formula: r = (s√3) / 6.
- Substituting the value of r we found: 4√3 = (s√3) / 6.
Solving for the Side Length
- Cross-multiplying gives: 4√3 * 6 = s√3.
- This simplifies to: s = 24 units.
Calculating the Perimeter of the Triangle
- The perimeter (P) of an equilateral triangle is given by: P = 3s.
- Substituting the side length: P = 3 * 24 = 72 units.
Conclusion
- The perimeter of the equilateral triangle is 72 units.
This detailed breakdown provides clarity on the relationship between the inscribed circle and the equilateral triangle, leading to the final answer.
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If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is?
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If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is?.
If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If area of a circle inscribed in a equilateral triangle is 48pi square units then perimeter of the triangle is?.
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