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In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?
- a)0.20
- b)0.33
- c)0.50
- d)0.60
- e)0.75
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In the given figure, ABC is an equilateral triangle such that AD= DB a...
Given
- ABC is an equilateral triangle
- DEGF is a quadrilateral with two angles of 90 each
- AD = DB
- DF || EG
- As DF || EG and ∠DEG = ∠FGE = 90 , ∠EDF = ∠DFG = 90
- So, DEFG is either a rectangle or a square
- A point P is selected at random inside the triangle
To Find: Probability of the point P lies inside the quadrilateral DEFG?
Approach
- Possible number of ways in which P can lie inside quadrilateral DEFG = Ar(DEFG)
- Total number of ways in which P can lie inside triangle ABC = Ar(ABC)
- Therefore, Probability of P lying inside DEFG =
- As we do not know the values of any of the sides, we will need to express the areas of both quadrilateral DEFG and triangle ABC in a common term
- For this purpose, let’s assume the length of side of triangle ABC to be x
- So, Ar(ABC) =
- So, we need to express the Ar(DEFG) in terms of x.
- As DEFG is a rectangle, we will try to express the sides of DEFG in terms of x
- To find the lengths of DEFG, we will focus on triangles ADE and EGC (as they have DE and EG as one of their sides)
- We will use the standard trigonometric ratios to express DE and EG in terms of x
Working Out
- In triangle EGC, we have ∠GCE = 60o and ∠EGC = 90o.
- So, that leaves us with ∠CEG = 30o
- However, we right now do not know any of the side lengths of this triangle.
- We know that AC is a straight line. So, ∠AED + ∠DEG + ∠CEG = 180o
- That gives us ∠AED = 60o
- In triangle ADE, we have ∠DAE = ∠AED = 60o
- So, ∠ADE = 60o
- Thus, ADE is an equilateral triangle with AD = DE = EA
- But we know that AD = DB = x/2
- So, we have DE =x/2….(1)
- Hence, we have one side of DEFG in terms of x
- Coming back to triangle EGC, as we have AE =
- , we can write EC =
- Thus, triangle EGC is a 30o- 60o– 90o triangle with one of the sides EC =
- 6. Hence probability of point P lying inside DEFG =
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In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. Can you explain this answer?
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In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. 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 In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. Can you explain this answer?.
In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. 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 In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?a)0.20b)0.33c)0.50d)0.60e)0.75Correct answer is option 'C'. Can you explain this answer?.
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