Railways Exam > Railways Questions > The semi-perimeter of a right-angled triangle...
Start Learning for Free
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?
- a)√(73) cm2
- b)10 cm2
- c)12 cm2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the sh...
Given: S = 12 cm & BP = 5 cm
∴ AP = PC = BP = 5 cm
∴ AC = 10 cm
We know the ratio of Right triangle like (3:4:5)
then we assume the ratio, (6:8:10)
So, the other two sides = 8 cm, 6 cm
∴ Area of △QBC = ½ x QB x BC = 1/2 x 4 x 6 = 12cm2
Most Upvoted Answer
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the sh...
Let the sides of the right-angled triangle be a, b, and c, with c being the hypotenuse.
We know that a^2 + b^2 = c^2 (Pythagorean theorem).
The semi-perimeter is given by (a+b+c)/2 = 12 cm.
The shortest median is given by (1/2)*sqrt(2*(a^2 + b^2) - c^2) = 5 cm.
From the first equation, we can express c in terms of a and b as c = sqrt(a^2 + b^2).
Substituting this into the second equation, we get (1/2)*sqrt(2*(a^2 + b^2) - (a^2 + b^2)) = 5 cm.
Simplifying, we get sqrt(a^2 + b^2) = 10 cm.
Squaring both sides, we get a^2 + b^2 = 100.
Using the semi-perimeter equation, we can express c in terms of a and b as c = 24 - a - b.
To find the largest median as the longest side, we want to maximize c.
Since a^2 + b^2 = 100, we can rewrite c as c = 24 - sqrt(100) = 14 cm.
The area of the triangle is (1/2)*a*b = (1/2)*(10)*(10) = 50 cm^2.
Therefore, the area of the triangle with the largest median as its longest side is 50 cm^2. Answer: a) 50.
We know that a^2 + b^2 = c^2 (Pythagorean theorem).
The semi-perimeter is given by (a+b+c)/2 = 12 cm.
The shortest median is given by (1/2)*sqrt(2*(a^2 + b^2) - c^2) = 5 cm.
From the first equation, we can express c in terms of a and b as c = sqrt(a^2 + b^2).
Substituting this into the second equation, we get (1/2)*sqrt(2*(a^2 + b^2) - (a^2 + b^2)) = 5 cm.
Simplifying, we get sqrt(a^2 + b^2) = 10 cm.
Squaring both sides, we get a^2 + b^2 = 100.
Using the semi-perimeter equation, we can express c in terms of a and b as c = 24 - a - b.
To find the largest median as the longest side, we want to maximize c.
Since a^2 + b^2 = 100, we can rewrite c as c = 24 - sqrt(100) = 14 cm.
The area of the triangle is (1/2)*a*b = (1/2)*(10)*(10) = 50 cm^2.
Therefore, the area of the triangle with the largest median as its longest side is 50 cm^2. Answer: a) 50.
Attention Railways Students!
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.
|
Explore Courses for Railways exam
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The semi-perimeter of a right-angled triangle ABC is 12 cm, and the shortest median is 5 cm. What is the area of the triangle which has the largest median of triangle ABC as its longest side?a)√(73) cm2b)10 cm2c)12 cm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup