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A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are natural numbers. What is the perimeter of the triangle?
(2012)
- a)30 cm
- b)26 cm
- c)28 cm
- d)32 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A circle of radius 6.5 cm is circumscribed around a right-angled trian...
Centre of the circle will be mid-point of the hypotenuse of the triangle.
So, hypotenuse = 2 × 6.5 = 13 cm.
According to Pythagorean triples.
other sides are 5 cm and 12 cm because all sides are natural number.
∴ So perimeter = 5 + 12 + 13 = 30 cm
So, hypotenuse = 2 × 6.5 = 13 cm.
According to Pythagorean triples.
other sides are 5 cm and 12 cm because all sides are natural number.
∴ So perimeter = 5 + 12 + 13 = 30 cm
Community Answer
A circle of radius 6.5 cm is circumscribed around a right-angled trian...
Given information:
- A circle of radius 6.5 cm is circumscribed around a right-angled triangle.
- The sides of the triangle are a, b, and c cm.
- a, b, and c are natural numbers.
To find:
- The perimeter of the triangle.
Approach:
- Since a circle is circumscribed around the triangle, the diameter of the circle will be equal to the hypotenuse of the triangle.
- Let the hypotenuse of the triangle be d cm.
- Then, according to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- So, we can write the equation as d^2 = a^2 + b^2.
- As the circle is circumscribed around the triangle, the diameter of the circle will be equal to the hypotenuse.
- Therefore, the diameter of the circle is 2d cm.
Calculation:
- The radius of the circle is given as 6.5 cm.
- Using the formula, radius = diameter/2, we can write 6.5 = 2d/2.
- Simplifying, we get d = 13 cm.
- Now, we can use the Pythagorean theorem to find the sides of the triangle.
- Since the hypotenuse is 13 cm, we have 13^2 = a^2 + b^2.
- Simplifying, we get a^2 + b^2 = 169.
- We need to find the perimeter of the triangle, which is the sum of all three sides.
- So, the perimeter will be a + b + c.
- Since a, b, and c are natural numbers, the possible values for a and b can be determined from the equation a^2 + b^2 = 169.
- The possible pairs of natural numbers that satisfy this equation are (5, 12) and (12, 5).
- Let's consider the pair (5, 12).
- In this case, a = 5, b = 12, and c = 13 (using the Pythagorean theorem).
- The perimeter of the triangle is 5 + 12 + 13 = 30 cm.
- Therefore, the correct answer is option A) 30 cm.
- A circle of radius 6.5 cm is circumscribed around a right-angled triangle.
- The sides of the triangle are a, b, and c cm.
- a, b, and c are natural numbers.
To find:
- The perimeter of the triangle.
Approach:
- Since a circle is circumscribed around the triangle, the diameter of the circle will be equal to the hypotenuse of the triangle.
- Let the hypotenuse of the triangle be d cm.
- Then, according to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- So, we can write the equation as d^2 = a^2 + b^2.
- As the circle is circumscribed around the triangle, the diameter of the circle will be equal to the hypotenuse.
- Therefore, the diameter of the circle is 2d cm.
Calculation:
- The radius of the circle is given as 6.5 cm.
- Using the formula, radius = diameter/2, we can write 6.5 = 2d/2.
- Simplifying, we get d = 13 cm.
- Now, we can use the Pythagorean theorem to find the sides of the triangle.
- Since the hypotenuse is 13 cm, we have 13^2 = a^2 + b^2.
- Simplifying, we get a^2 + b^2 = 169.
- We need to find the perimeter of the triangle, which is the sum of all three sides.
- So, the perimeter will be a + b + c.
- Since a, b, and c are natural numbers, the possible values for a and b can be determined from the equation a^2 + b^2 = 169.
- The possible pairs of natural numbers that satisfy this equation are (5, 12) and (12, 5).
- Let's consider the pair (5, 12).
- In this case, a = 5, b = 12, and c = 13 (using the Pythagorean theorem).
- The perimeter of the triangle is 5 + 12 + 13 = 30 cm.
- Therefore, the correct answer is option A) 30 cm.
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A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer?.
A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are naturalnumbers. What is the perimeter of the triangle?(2012)a)30 cmb)26 cmc)28 cmd)32 cmCorrect answer is option 'A'. Can you explain this answer?.
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