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Triangle ABC is an isosceles triangle with AB = AC and AD is the perpendicular dropped from vertex A on the side BC. What is the perimeter of triangle ABC?
(1) ∠BAD = 2∠ACD
(2) The perimeter of triangle ADB is 15 + 5√3
  • 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?

Answers

Steps 1 & 2: Understand Question and Draw Inferences
Given:
  • Isosceles ΔABC
    • AB = AC
    • So, perpendicular AD will bisect side BC.
    • If we assume ∠ ABC to be xo, the different ∠s in the figure can be represented as below:
 
To find: Perimeter of ΔABC
  • =AB + BC + CA
  • = 2AB + BC
So, in order to find the perimeter, we need to know AC and BC
Knowing the ∠s may help us (because we may then employ trigonometric ratios)
 
Step 3: Analyze Statement 1 independently
 
(1) ∠BAD = 2∠ACD
90°- x° = 2x° 
⇒ 3x° = 90°  
⇒ x° = 30°
But we don’t know the magnitude of any side of the triangle. So, we cannot yet use trigonometric ratios to find the sides of the triangle.
Not sufficient.
Step 4: Analyze Statement 2 independently
(2) The perimeter of triangle ADB is 15 + 5√3
The value of 2AB + BC depends on the value of AD.
Since we do not know the value of AD, we cannot find the required value
Not sufficient.
  • From Statement 2 
 
  • Using Equation II, a unique value of AD will be obtained
  • Using Equation I, the value of 2AB + BC will be obtained
Sufficient.
Answer: Option C

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Triangle ABC is an isosceles triangle with AB = AC and AD is the perpendicular dropped from vertex A on the side BC. What is the perimeter of triangle ABC?(1) ∠BAD = 2∠ACD(2) The perimeter of triangle ADB is 15 + 5√3a)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? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Triangle ABC is an isosceles triangle with AB = AC and AD is the perpendicular dropped from vertex A on the side BC. What is the perimeter of triangle ABC?(1) ∠BAD = 2∠ACD(2) The perimeter of triangle ADB is 15 + 5√3a)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? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is an isosceles triangle with AB = AC and AD is the perpendicular dropped from vertex A on the side BC. What is the perimeter of triangle ABC?(1) ∠BAD = 2∠ACD(2) The perimeter of triangle ADB is 15 + 5√3a)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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Steps 1 2: Understand Question and Draw InferencesGiven: Isosceles ABC AB = AC So, perpendicular AD will bisect side BC. If we assume ABC to be xo, the different s in the figure can be represented as below: To find: Perimeter of ABC =AB + BC + CA = 2AB + BCSo, in order to find the perimeter, we need to know AC and BCKnowing the s may help us (because we may then employ trigonometric ratios)Step 3: Analyze Statement 1 independently(1) BAD = 2ACD90- x = 2x 3x = 90 x = 30But we dont know the magnitude of any side of the triangle. So, we cannot yet use trigonometric ratios to find the sides of the triangle.Not sufficient.Step 4: Analyze Statement 2 independently(2) The perimeter of triangle ADB is 15 + 53The value of 2AB + BC depends on the value of AD.Since we do not know the value of AD, we cannot find the required valueNot sufficient. From Statement 2 Using Equation II, a unique value of AD will be obtained Using Equation I, the value of 2AB + BC will be obtainedSufficient.Answer: Option C