Question: In the figure shown above, what is the perimeter of parallelogram ABCD?

1. 12
2. \(10 + 6 \sqrt 2\)
3. \(20 + \sqrt 2\)
4. 24
5. Not enough information

Answer:
Solution with Explanation:
Approach Solution (1):

The line AB is at 45 degrees to a horizontal, and it passes through the origin, so it is line y = x. since point B has the same y- coordinate as (8, 3), and is on line AB, it must be the point (3, 3).

So the two horizontal sides of the parallelogram are 5 units long (since 8 – 3 = 3).

If you draw a vertical line down from point B to the x- axis, you get a 45-45-90 right triangle with short sides of length 3, so the hypotenuse AB is \(3 \sqrt2\).

So the two sloping sides of parallelogram have a combined length of \(6 \sqrt2\), and adding the two horizontal sides, the perimeter is \(10 + 6 \sqrt 2\).

Correct Option: B

Approach Solution (2):

Given: C = (8, 3) drop a line tp x axis

We get 45 : 45 : 90; x : x : \( x \sqrt2\) ; so CD = \(3 \sqrt2\)

Also at B do same, we get B; 3, 3, so BC; 5 units and AB; \(3 \sqrt 2\) and AD = 5

Perimeter: 5 + 5 + \(3 \sqrt 2\); 10 + \(6 \sqrt 2\)

Correct Option: B

“In the figure shown above, what is the perimeter of parallelogram ABCD?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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