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The length of the circum-radius of a triangle having sides of lengths 12 cm, 16 cm and 20 cm is (SSC CGL 2nd Sit. 2012)
- a)15 cm
- b)10 cm
- c)18 cm
- d)16 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The length of the circum-radius of a triangle having sides of lengths ...
Let the sides a = 12 cm, b = 16cm, c = 20 cm then,
there, a2 + b2 = c2
(12)2 + (16)2 = (20)2
144 + 256 = 400
400 = 400
∴ ΔABC is a right angle triangle, whose hypotenuse
AB = 20 cm.
As we know that the Length of the diameter of outer circle of right angle triangle is equal to its hypotenuse.
So, radius of required circle = 20/2 = 10 cm.
there, a2 + b2 = c2
(12)2 + (16)2 = (20)2
144 + 256 = 400
400 = 400
∴ ΔABC is a right angle triangle, whose hypotenuse
AB = 20 cm.
As we know that the Length of the diameter of outer circle of right angle triangle is equal to its hypotenuse.
So, radius of required circle = 20/2 = 10 cm.
Most Upvoted Answer
The length of the circum-radius of a triangle having sides of lengths ...
To find the circum-radius of a triangle, we can use the formula:
R = (abc) / (4A)
Where R is the circum-radius, a, b, and c are the lengths of the sides of the triangle, and A is the area of the triangle.
In this case, we have a triangle with side lengths 12 cm, 16 cm, and 20 cm.
Step 1: Finding the Area of the Triangle
To find the area of the triangle, we can use Heron's formula:
A = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle, which is calculated as:
s = (a + b + c) / 2
Substituting the given side lengths into the formula, we have:
s = (12 + 16 + 20) / 2
s = 24
Now, we can calculate the area of the triangle:
A = √(24(24-12)(24-16)(24-20))
A = √(24(12)(8)(4))
A = √(9216)
A = 96 cm²
Step 2: Finding the Circum-Radius
Now that we have the area of the triangle, we can calculate the circum-radius using the formula:
R = (abc) / (4A)
Substituting the given side lengths and the calculated area, we have:
R = (12 * 16 * 20) / (4 * 96)
R = 3840 / 384
R = 10 cm
Therefore, the length of the circum-radius of the triangle is 10 cm.
R = (abc) / (4A)
Where R is the circum-radius, a, b, and c are the lengths of the sides of the triangle, and A is the area of the triangle.
In this case, we have a triangle with side lengths 12 cm, 16 cm, and 20 cm.
Step 1: Finding the Area of the Triangle
To find the area of the triangle, we can use Heron's formula:
A = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle, which is calculated as:
s = (a + b + c) / 2
Substituting the given side lengths into the formula, we have:
s = (12 + 16 + 20) / 2
s = 24
Now, we can calculate the area of the triangle:
A = √(24(24-12)(24-16)(24-20))
A = √(24(12)(8)(4))
A = √(9216)
A = 96 cm²
Step 2: Finding the Circum-Radius
Now that we have the area of the triangle, we can calculate the circum-radius using the formula:
R = (abc) / (4A)
Substituting the given side lengths and the calculated area, we have:
R = (12 * 16 * 20) / (4 * 96)
R = 3840 / 384
R = 10 cm
Therefore, the length of the circum-radius of the triangle is 10 cm.
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Community Answer
The length of the circum-radius of a triangle having sides of lengths ...
Let the sides a = 12 cm, b = 16cm, c = 20 cm then,
there, a2 + b2 = c2
(12)2 + (16)2 = (20)2
144 + 256 = 400
400 = 400
∴ ΔABC is a right angle triangle, whose hypotenuse
AB = 20 cm.
As we know that the Length of the diameter of outer circle of right angle triangle is equal to its hypotenuse.
So, radius of required circle = 20/2 = 10 cm.
there, a2 + b2 = c2
(12)2 + (16)2 = (20)2
144 + 256 = 400
400 = 400
∴ ΔABC is a right angle triangle, whose hypotenuse
AB = 20 cm.
As we know that the Length of the diameter of outer circle of right angle triangle is equal to its hypotenuse.
So, radius of required circle = 20/2 = 10 cm.
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