If parallelogram ABCD has a perimeter of 12 u...
If parallelogram ABCD has a perimeter of 12 units and ∠ADC = 120 , what is the area of the parallelogram?
(1) BD = 2√3 units
(2) The distance between sides AB and CD is √3 units
• 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
• 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 'D'. Can you explain this answer?

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 Mittul Madaan Apr 15, 2020
Step 1 & 2: Understand Question and Draw Inference
Given
• ABCD is a parallelogram.
• Let AB and CD measure p units and AD and BC measure q units
• 2(p + q) = 12
• p + q = 6 . . . (I)
• ∠ADC = 120
• Using the properties of parallel lines, we can mark the other ∠s of the parallelogram as below:

To Find : Area of the parallelogram
• Area = p * h, where h is the perpendicular distance between the base and the side opposite to it.
• Since ΔAED is a 30-60-90 triangle, applying the angle-side property
Step 3 : Analyze Statement 1 independent
BD = 2√3 units
• In right ΔAED, applying side ratio property of 30-60-90 triangle, we get
• Since we get a unique value of Area, Statement 1 is sufficient to answer
Step 4 : Analyze Statement 2 independent
h= √3 units
• From Equation II, q = 2
• From Equation I, p = 4
• Since we now know the value of p and q, we can find the value of product pq, and hence of the area of the parallelogram, using Equation III
• Hence, even Statement 2 is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Steps 3 and 4 each, this step
is not required
Hence the correct answer is Option D .

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 Notes Wala Feb 17, 2022
Step 1 & 2: Understand Question and Draw Inference
Given
• ABCD is a parallelogram.
• Let AB and CD measure p units and AD and BC measure q units
• 2(p + q) = 12
• p + q = 6 . . . (I)
• ∠ADC = 120
• Using the properties of parallel lines, we can mark the other ∠s of the parallelogram as below:

To Find : Area of the parallelogram
• Area = p * h, where h is the perpendicular distance between the base and the side opposite to it.
• Since ΔAED is a 30-60-90 triangle, applying the angle-side property
Step 3 : Analyze Statement 1 independent
BD = 2√3 units
• In right ΔAED, applying side ratio property of 30-60-90 triangle, we get
• Since we get a unique value of Area, Statement 1 is sufficient to answer
Step 4 : Analyze Statement 2 independent
h= √3 units
• From Equation II, q = 2
• From Equation I, p = 4
• Since we now know the value of p and q, we can find the value of product pq, and hence of the area of the parallelogram, using Equation III
• Hence, even Statement 2 is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Steps 3 and 4 each, this step
is not required
Hence the correct answer is Option D .

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