Triangle ABC is an isosceles triangle with AB...

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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?
(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)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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

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.

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