EgmatQuantExpert wrote:
Q. 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 \(15 + 5√3\)
Answer Choices :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.
Thanks,
Saquib
Quant Expert
e-GMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
(1) \(∠BAD = 2∠ACD\)
From the above statement, we conclude that ∠BAD = 60 and ∠ABD = 30. Since the triangle ADB is a right triangle, the ratio should be 1: √3 : 2. However, no lengths are defined in this statement. Insufficient.
2) The perimeter of triangle ADB is \(15 + 5√3\)[/list]
No angles are defined. Only the sum of sides, AD + DB + AB = 15 + 5√3. Clearly insufficient.
Combining the two, we get the ratio of lengths and equate it total lengths.
x + √3x + 2x = 15 + 5√3 => x = 5. This should be sufficient to figure out the perimeter.