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Solve the following question and mark the best possible option.
In right-angled ∆ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?
- a)(a - b)2 = 2ab
- b)(a - b)2 = 4ab
- c)(a + b)2 = 4ab
- d)(a + b)2 = 2ab
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Solve the following question and mark the best possible option.In righ...
Since the median c / 2 is the GM of a and b.
We have ab = (c / 2)2 ⇒ 4ab = c2.
We have ab = (c / 2)2 ⇒ 4ab = c2.
Using the pythagorean theorem
We know that c2 = a2+b2 = 4ab
⇒ a2 - 2ab + b2 = 2ab
⇒ (a - b)2 = 2ab
We know that c2 = a2+b2 = 4ab
⇒ a2 - 2ab + b2 = 2ab
⇒ (a - b)2 = 2ab
Most Upvoted Answer
Solve the following question and mark the best possible option.In righ...
Given:
In right-angled triangle ABC, a and b are the lengths of the legs of the right angle, and c is the length of the hypotenuse. The length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle.
To find:
Which of the following is true?
Solution:
Let's consider the right-angled triangle ABC.
Median to the Hypotenuse:
The median to the hypotenuse of a right-angled triangle is half the length of the hypotenuse. Therefore, the length of the median to the hypotenuse is c/2.
Geometric Mean:
The geometric mean of two numbers a and b is the square root of their product. Therefore, the geometric mean of the lengths of the legs of the right angle is √(a * b).
Equation:
According to the given information, the length of the median to the hypotenuse is equal to the geometric mean of the lengths of the legs of the right angle. Therefore, we can write the equation as:
c/2 = √(a * b)
Squaring both sides of the equation:
(c/2)^2 = (√(a * b))^2
(c/2)^2 = a * b
c^2/4 = a * b
Manipulating the equation:
Multiplying both sides of the equation by 4, we get:
c^2 = 4 * a * b
Comparing with the options:
Now let's compare the obtained equation with the given options.
a) (a - b)^2 = 2ab
This option does not match the obtained equation.
b) (a - b)^2 = 4ab
This option does not match the obtained equation.
c) (a + b)^2 = 4ab
This option does not match the obtained equation.
d) (a + b)^2 = 2ab
This option does not match the obtained equation.
Therefore, the correct option is a) (a - b)^2 = 2ab.
In right-angled triangle ABC, a and b are the lengths of the legs of the right angle, and c is the length of the hypotenuse. The length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle.
To find:
Which of the following is true?
Solution:
Let's consider the right-angled triangle ABC.
Median to the Hypotenuse:
The median to the hypotenuse of a right-angled triangle is half the length of the hypotenuse. Therefore, the length of the median to the hypotenuse is c/2.
Geometric Mean:
The geometric mean of two numbers a and b is the square root of their product. Therefore, the geometric mean of the lengths of the legs of the right angle is √(a * b).
Equation:
According to the given information, the length of the median to the hypotenuse is equal to the geometric mean of the lengths of the legs of the right angle. Therefore, we can write the equation as:
c/2 = √(a * b)
Squaring both sides of the equation:
(c/2)^2 = (√(a * b))^2
(c/2)^2 = a * b
c^2/4 = a * b
Manipulating the equation:
Multiplying both sides of the equation by 4, we get:
c^2 = 4 * a * b
Comparing with the options:
Now let's compare the obtained equation with the given options.
a) (a - b)^2 = 2ab
This option does not match the obtained equation.
b) (a - b)^2 = 4ab
This option does not match the obtained equation.
c) (a + b)^2 = 4ab
This option does not match the obtained equation.
d) (a + b)^2 = 2ab
This option does not match the obtained equation.
Therefore, the correct option is a) (a - b)^2 = 2ab.
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Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer?
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Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer?.
Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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ample number of questions to practice Solve the following question and mark the best possible option.In right-angled ABC, a and b are the lengths of the legs of the right angle and c is the length of the hypotensue. If the length of the median to the hypotenuse is the geometric mean of the lengths of the legs of the right angle, which of the following is true?a)(a - b)2 = 2abb)(a - b)2 = 4abc)(a + b)2 = 4abd)(a + b)2 = 2abCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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