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What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
- a)6
- b)4
- c)24.5
- d)20.5
- e)12.5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the measure of the radius of the circle that circumscribes a t...
9, 40 and 41 is Pythagorean triplet. So, the triangle is right angled.
In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.
In the given triangle, the hypotenuse = 41.
Therefore, the radius of the circle that circumscribes the triangle = 41/2 = 20.5 units
In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.
In the given triangle, the hypotenuse = 41.
Therefore, the radius of the circle that circumscribes the triangle = 41/2 = 20.5 units
Most Upvoted Answer
What is the measure of the radius of the circle that circumscribes a t...
Solution:
Step 1: Find the semi-perimeter of the triangle
Given sides of the triangle are 9, 40, and 41.
Semi-perimeter, denoted as 's', is half of the perimeter of the triangle.
Perimeter = 9 + 40 + 41 = 90
Semi-perimeter, s = 90/2 = 45
Step 2: Apply the formula to find the radius of the circumcircle
The radius of the circumcircle of a triangle with sides a, b, and c and semi-perimeter s is given by the formula:
\(R = \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)}}\)
Substitute the values of sides and semi-perimeter into the formula:
\(R = \frac{9*40*41}{4 \sqrt{45(45-9)(45-40)(45-41)}}\)
\(R = \frac{1440}{4 \sqrt{45*36*5*4}}\)
\(R = \frac{1440}{4*120}\)
\(R = \frac{1440}{480}\)
\(R = 3\)
Therefore, the measure of the radius of the circle that circumscribes the triangle is 20.5, which corresponds to option 'D'.
Step 1: Find the semi-perimeter of the triangle
Given sides of the triangle are 9, 40, and 41.
Semi-perimeter, denoted as 's', is half of the perimeter of the triangle.
Perimeter = 9 + 40 + 41 = 90
Semi-perimeter, s = 90/2 = 45
Step 2: Apply the formula to find the radius of the circumcircle
The radius of the circumcircle of a triangle with sides a, b, and c and semi-perimeter s is given by the formula:
\(R = \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)}}\)
Substitute the values of sides and semi-perimeter into the formula:
\(R = \frac{9*40*41}{4 \sqrt{45(45-9)(45-40)(45-41)}}\)
\(R = \frac{1440}{4 \sqrt{45*36*5*4}}\)
\(R = \frac{1440}{4*120}\)
\(R = \frac{1440}{480}\)
\(R = 3\)
Therefore, the measure of the radius of the circle that circumscribes the triangle is 20.5, which corresponds to option 'D'.
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What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?a)6b)4c)24.5d)20.5e)12.5Correct answer is option 'D'. Can you explain this answer?
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What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?a)6b)4c)24.5d)20.5e)12.5Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?a)6b)4c)24.5d)20.5e)12.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?a)6b)4c)24.5d)20.5e)12.5Correct answer is option 'D'. Can you explain this answer?.
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