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A right angled triangle, right angled at point B has angles such that a<c<b where a, b, c correspond to the angles at points A, B, C. If the area of the triangle is 2 which of the following inequality indicates the range of values of side BC.
  • a)
    0 < BC < 2
  • b)
    0 < BC < √2
  • c)
    0 < BC < 4
  • d)
    0<BC < 2√2
  • e)
    0 < BC < 8
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A right angled triangle, right angled at point B has angles such that ...
Since it is given that ΔABC is right angled at B, Angle ABC = 90
Also, area of ΔABC = ½ * AB * BC = 2
AB*BC = 4
But it is given that a < c
Therefore, BC < AB
In the extreme case of BC = AB (which is not possible according to the given condition),
BC = AB = 2
However, since BC < AB
BC should be less than 2 and AB should be greater than 2.
Therefore, BC < 2
Also, since BC is a side of a triangle, it is positive and greater than zero
Therefore, BC > 0
Combining the above two inequalities, we get:
0 < BC < 2
Correct Answer: A
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Most Upvoted Answer
A right angled triangle, right angled at point B has angles such that ...
Solution:
Given, a right angled triangle ABC, right angled at point B with angles such that acb where a, b, c correspond to the angles at points A, B, C and the area of the triangle is 2.

Let AB = x and BC = y.

Then, AC = √(x^2 + y^2) (by Pythagoras theorem)

Area of the triangle ABC = (1/2) * AB * BC = (1/2) * x * y = 2

x * y = 4

Now, we need to find the range of values of BC.

Range of values of BC can be found using the following inequality:

(1/2) * AB * BC <= 2="" (area="" of="" the="" triangle="" abc="" is="" less="" than="" or="" equal="" to="">

Substituting AB = x and BC = y, we get:

(1/2) * x * y <=>

x * y <=>

Therefore, the range of values of BC is:

0 < bc="" /><= 2="" (since="" x="" *="" y="">

Hence, the correct option is A.

Answer: A
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A right angled triangle, right angled at point B has angles such that a<c<b where a, b, c correspond to the angles at points A, B, C. If the area of the triangle is 2 which of the following inequality indicates the range of values of side BC.a)0 < BC < 2b)0 < BC < √2c)0 < BC < 4d)0<BC < 2√2e)0 < BC < 8Correct answer is option 'A'. Can you explain this answer?
Question Description
A right angled triangle, right angled at point B has angles such that a<c<b where a, b, c correspond to the angles at points A, B, C. If the area of the triangle is 2 which of the following inequality indicates the range of values of side BC.a)0 < BC < 2b)0 < BC < √2c)0 < BC < 4d)0<BC < 2√2e)0 < BC < 8Correct answer is option 'A'. 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 A right angled triangle, right angled at point B has angles such that a<c<b where a, b, c correspond to the angles at points A, B, C. If the area of the triangle is 2 which of the following inequality indicates the range of values of side BC.a)0 < BC < 2b)0 < BC < √2c)0 < BC < 4d)0<BC < 2√2e)0 < BC < 8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right angled triangle, right angled at point B has angles such that a<c<b where a, b, c correspond to the angles at points A, B, C. If the area of the triangle is 2 which of the following inequality indicates the range of values of side BC.a)0 < BC < 2b)0 < BC < √2c)0 < BC < 4d)0<BC < 2√2e)0 < BC < 8Correct answer is option 'A'. Can you explain this answer?.
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