A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 43 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer?

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A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?

(1) Triangle ABC is an equilateral triangle

(2) The area of Triangle ABC is 4√3 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

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

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Test: Rectangles And Squares- 1

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A triangle ABC is placed inside a rectangle PQRS such that the minimum...

Steps 1 and 2 – Understand the question statement and draw inferences

To find – Area of rectangle PQRS given the conditions about triangle ABC.

Given – Minimum distance from any vertex of the triangle to the frame = 2”.

The Area of the Rectangle = PQ*PS . . . (1)

So, in order to find the area, we need to know the values of PQ and PS.

Now, from the given diagram, it’s clear that PQ = 2 + AB +2

That is, PQ = AB + 4 . . . (2)

Similarly, let’s try to express PS in terms of a dimension of the triangle ABC. (Note: We are expressing the dimensions of the rectangle in terms of the dimensions of the triangle because both St. 1 and 2 give us information regarding the triangle only)

Let’s drop a perpendicular CD from C on the side AB.

By doing so, we get: PS = 2 + CD + 2

That is, PS = CD + 4 . . . (3)

Substituting (2) and (3) in (1), we get:

Area of rectangle = (AB+4)(CD+4) . . . (4)

Thus, in order to find the area of rectangle PQRS, we need to find the values of AB and CD.

With this understanding, let’s analyze the given statements.

Step 3 – Analyse Statement (1)

Per statement (1), Triangle ABC is an equilateral triangle.

This means, AB = BC = AC

And, CD = √3/2 * AB

However, since this statement doesn’t provide us the exact value of AB, we will not be able to find the area of rectangle PQRS.

Therefore, statement 1 does not provide sufficient information to arrive at a unique answer.

Step 4 – Analyse Statement (2)

Statement 2 provides two pieces of information

Area of Triangle ABC = 4√3 in².
AB = 50% of PQ.

Area of triangle ABC = ½ * AB * CD = 4√3

AB * CD = 8√3 ….(5)

Also,

AB = 0.5 * PQ
2AB = AB + 4
AB = 4 . . . (6)

Substituting (6) in (5), we get:

4CD = 8√3

So, CD = 2√3 . . .(7)

Substituting (6) and (7) in (4), we can find the area of rectangle PQRS.

Thus, St. 2 is sufficient to determine the area of the rectangle.

Step 5 – Analyze both Statements together

This step is not required since statement 2 helps us arrive at a unique answer.

Correct Answer – Choice B

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A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 4√3 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer?

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A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 4√3 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. 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 A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 4√3 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 4√3 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer?.

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