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In a triangle ABC, a = 13, b = 14, c = 15, then r1 =
a) 21/2
b) 14
C) 65/8
d) 4
Correct answer is option 'A'. Can you explain this answer?
a) 21/2
b) 14
C) 65/8
d) 4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d)...
R=∆/s
∆=√[(s)(s-a)(s-b)(s-c)]
s=(a+b+c)/2=42/2=21
∆=√[21×8×7×6] = 7×3×4 = 84
r=84/21=4
∆=√[(s)(s-a)(s-b)(s-c)]
s=(a+b+c)/2=42/2=21
∆=√[21×8×7×6] = 7×3×4 = 84
r=84/21=4
Most Upvoted Answer
In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d)...
Given:
Triangle ABC with side lengths: a = 13, b = 14, c = 15
To Find:
The value of r1
Solution:
The radius of the inscribed circle in a triangle is given by the formula:
r1 = A / s
Where A is the area of the triangle and s is the semi-perimeter of the triangle.
Step 1: Calculate the semi-perimeter (s) of the triangle:
s = (a+b+c)/2 = (13+14+15)/2 = 21
Step 2: Calculate the area (A) of the triangle using Heron's formula:
A = sqrt(s(s-a)(s-b)(s-c))
Substituting the given values into the formula:
A = sqrt(21(21-13)(21-14)(21-15))
= sqrt(21(8)(7)(6))
= sqrt(21 * 8 * 7 * 6)
= sqrt(2^2 * 3 * 7 * 2^3 * 7 * 3)
= sqrt(2^5 * 3^2 * 7^2)
= 2^2 * 3 * 7
= 4 * 3 * 7
= 84
Step 3: Substitute the values of A and s into the formula for r1:
r1 = A / s
= 84 / 21
= 4
Therefore, the value of r1 is 4.
Answer:
The correct option is (d) 4.
Triangle ABC with side lengths: a = 13, b = 14, c = 15
To Find:
The value of r1
Solution:
The radius of the inscribed circle in a triangle is given by the formula:
r1 = A / s
Where A is the area of the triangle and s is the semi-perimeter of the triangle.
Step 1: Calculate the semi-perimeter (s) of the triangle:
s = (a+b+c)/2 = (13+14+15)/2 = 21
Step 2: Calculate the area (A) of the triangle using Heron's formula:
A = sqrt(s(s-a)(s-b)(s-c))
Substituting the given values into the formula:
A = sqrt(21(21-13)(21-14)(21-15))
= sqrt(21(8)(7)(6))
= sqrt(21 * 8 * 7 * 6)
= sqrt(2^2 * 3 * 7 * 2^3 * 7 * 3)
= sqrt(2^5 * 3^2 * 7^2)
= 2^2 * 3 * 7
= 4 * 3 * 7
= 84
Step 3: Substitute the values of A and s into the formula for r1:
r1 = A / s
= 84 / 21
= 4
Therefore, the value of r1 is 4.
Answer:
The correct option is (d) 4.
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In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d)...
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In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d) 4Correct answer is option 'A'. Can you explain this answer?
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In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d) 4Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d) 4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC, a = 13, b = 14, c = 15, then r1=a)21/2b) 14C)65/8d) 4Correct answer is option 'A'. Can you explain this answer?.
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