Rectangle DEFG is inscribed in equilateral triangle as shown above. What is the area of triangle ABC?(1) The area of rectangle DEFG is 83 square units(2) The area of triangle AGD is 23 square unitsa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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a)
Statement (1) ALONE is sufficient, but statement (2) alone is
not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is
not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to
answer the question asked, but NEITHER statement ALONE
is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question
asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to
answer the question asked, and additional data specific to the
problem are needed.

Correct answer is option 'C'. Can you explain this answer?

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Rectangle DEFG is inscribed in equilateral triangle as shown above. Wh...

Ans.

Option (c)

Area of equilateral triangle =sqrt(3)*AB^2 / 4

So AB=?

Statement 1:
DG*GF=8*sqrt(3)
Insufficient

Statement 2:
1/2*AG*DG=2*sqrt(3)

We know ADG is a 30-60-90 triangle
So AG*AG*sqrt(3)=4*sqrt(3)
AG=2
DG=2*sqrt(3)

Insufficient
Statement 1&2:
2*sqrt(3)*GF=8*sqrt(3)
GF=4

We know that
BF=AG=2

Therefore AB= 2+2+4=8

Area= sqrt(3)*8^2 /4 = 16*sqrt(3)
Sufficient C

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Most Upvoted Answer

Rectangle DEFG is inscribed in equilateral triangle as shown above. Wh...

Step 1 & 2: Understand Question and Draw Inference

Given

ΔABC is equilateral
- ∠ABC = ∠BAC = ∠ACB = 60°
- Points D, E, F, G lie on the triangle
DEFG is a rectangle
- Each ∠ of this rectangle is 90°

To find the area, we need to find AB
Let’s represent the relation between different sides and ∠s of the figure:
∠CDE = ∠ CAB = 60° (corresponding ∠s)
- (Since the opposite sides of a rectangle are parallel, DE || GF, and therefore, DE || AB)
Similarly, ∠ CED = ∠ CBA = 60°.

Assuming the sides of the rectangle:
- GF = x units
- GD = EF = y units.
Expressing all the unknown lengths in terms of x and y:
- In equilateral ΔDEC, CD = CE = side DE of the rectangle = x
- ΔEFB is a 30-60-90 triangle
  - Hence we can write : FB : EF : EB = 1 : √3 : 2

Exactly corresponding calculations will also apply in right ΔDGA

Thus, in order to find the area of the triangle, we need to know the value of x and y.

Step 3 : Analyze Statement 1 independent

The area of rectangle DEFG is 8√3 square units

Multiple values of x and y will satisfy this equation.
Hence, Statement 1 is not sufficient.

Step 4 : Analyze Statement 2 independent

The area of triangle AGD is 2√3 square units

But we don’t know the value of x.
Hence, Statement 2 is also not sufficient.

Step 5: Analyze Both Statements Together (if needed)

Since we now know the value of x and y, we can find the value of AB.
Hence, by combining both the statement we can get our answer.

Therefore, the correct answer is Option C

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Community Answer

Rectangle DEFG is inscribed in equilateral triangle as shown above. Wh...

Step 1 & 2: Understand Question and Draw Inference

Given

ΔABC is equilateral
- ∠ABC = ∠BAC = ∠ACB = 60°
- Points D, E, F, G lie on the triangle
DEFG is a rectangle
- Each ∠ of this rectangle is 90°

To find the area, we need to find AB
Let’s represent the relation between different sides and ∠s of the figure:
∠CDE = ∠ CAB = 60° (corresponding ∠s)
- (Since the opposite sides of a rectangle are parallel, DE || GF, and therefore, DE || AB)
Similarly, ∠ CED = ∠ CBA = 60°.

Assuming the sides of the rectangle:
- GF = x units
- GD = EF = y units.
Expressing all the unknown lengths in terms of x and y:
- In equilateral ΔDEC, CD = CE = side DE of the rectangle = x
- ΔEFB is a 30-60-90 triangle
  - Hence we can write : FB : EF : EB = 1 : √3 : 2

Exactly corresponding calculations will also apply in right ΔDGA

Thus, in order to find the area of the triangle, we need to know the value of x and y.

Step 3 : Analyze Statement 1 independent

The area of rectangle DEFG is 8√3 square units

Multiple values of x and y will satisfy this equation.
Hence, Statement 1 is not sufficient.

Step 4 : Analyze Statement 2 independent

The area of triangle AGD is 2√3 square units

But we don’t know the value of x.
Hence, Statement 2 is also not sufficient.

Step 5: Analyze Both Statements Together (if needed)

Since we now know the value of x and y, we can find the value of AB.
Hence, by combining both the statement we can get our answer.

Therefore, the correct answer is Option C

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Rectangle DEFG is inscribed in equilateral triangle as shown above. What is the area of triangle ABC?(1) The area of rectangle DEFG is 8√3 square units(2) The area of triangle AGD is 2√3 square unitsa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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Rectangle DEFG is inscribed in equilateral triangle as shown above. What is the area of triangle ABC?(1) The area of rectangle DEFG is 8√3 square units(2) The area of triangle AGD is 2√3 square unitsa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Rectangle DEFG is inscribed in equilateral triangle as shown above. What is the area of triangle ABC?(1) The area of rectangle DEFG is 8√3 square units(2) The area of triangle AGD is 2√3 square unitsa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rectangle DEFG is inscribed in equilateral triangle as shown above. What is the area of triangle ABC?(1) The area of rectangle DEFG is 8√3 square units(2) The area of triangle AGD is 2√3 square unitsa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.

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