If quadrilateral ABCD, pictured above, has a perimeter of 64, what is

Question

https://gmatclub.com/forum/download/file.php?id=25359 If quadrilateral ABCD, pictured above, has a perimeter of 64, what is the length of line segment AD? (1) The length of line segment AD is equal to the length of line segment BC (2) Line segment AD is perpendicular to line segment BC Kudos for a correct solution . Quadrilateral.png

gmat6nplus1 · Answer

Basically we want to know whether quadrilateral ABCD is a square. 1) I generally don't trust gmat's shapes, but this time I will give it a try. If the two diagonals have the same lenght and bisect each other the shape is a square. And thus this statement would be sufficient. If I chose to be wary, I still don't know whether the two diagonals bisect each other, opening the likelyhood to have a wonky shape that can resemble a rhombus. What makes me doubt about my second scenario is that all the quadrilateral's angles are 90 degrees, suggesting that the shape is a quare (it can't be a rectangle since the diagonals have the same lenght). If we move the diagonal as in scenario two the angles are goin to reflect that and won't be 90 degrees anymore. 2) AD is perpendicular to BC. Not sufficient. The shape can either be a square or be a rhombus. Answer A. Please correct me if I am wrong

thanks in advance,

Icerockboom · Answer

If the quadrilateral ABCD is a square like the picture. Don't need any statement to get the measurement of AD.

mehtakaustubh · Answer

IMO B
A: Digonals are equal.. Not sufficient. As the given Quadrilaterial can be a square or rectangle.
B: Digonals are at right angle.
Also given thet sides are at right angle
Therefore the given quadrilaterial is a square
Therefore the length of diagnol can be founs.
Sufficient
IMO B.

EMPOWERgmatRichC · Answer

Hi Icerockbottom,

In DS questions, you CANNOT trust the picture. However, you CAN trust whatever factual information you're given to work with. We're told that the shape is a QUADRILATERAL and we can see four 90 degree angles. This means that the shape is either a SQUARE or a RECTANGLE.

For future reference, the prompt will NEVER give you enough information to answer the question on its own. You will need MORE information - whether the two Facts provide that necessary information is for you to determine.

Hi gmat6nplus1,

There's an easy way to test your ideas about diagonals, squares and rectangles. Draw a square and number the sides (for example, 5 and 5). What length are the two diagonals? Next, draw a rectangle and number the sides (for example, 3 and 4). What length are the two diagonals?

GMAT assassins aren't born, they're made,
Rich

DesiGmat · Answer

Here we go ----

Looking at the picture attached we can say that angles A, B, C, and D are 90 each.

So ABCD is a parallelogram - Both the pair of opposite angles are equal.
and parallelogram in which all the 4 angles are equal, each being 90, is a rectangle.

2 (L + B) = 64 ------(1)

AD^2 = L^2 + B^2 ------ (2)

St1: The length of line segment AD is equal to the length of line segment BC

Well, in any rectangle the diagonals are equal.

Clearly not sufficient

St2: Line segment AD is perpendicular to line segment BC

So we have two equal diagonals(property of a rectangle) and perpendicular to each other.

Hence, ABCD is a square.

From (1)

2(L + B) = 64
as L = B (all sides are equal in square)

2(2L) = 64 ----> L = 16

AD^2 = 16^2 + 16^2----------> 4sqrt(2)

Hence Option B is clearly sufficient

option B is correct

gmat6nplus1 · Answer

Hehe, you're right! I got it now. Thanks Rich!

Icerockboom · Answer

Thanks Rich

So the answer must be B.

Statement 2 makes ABDC a square.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Statement 1 is not sufficient, as that fact (the diagonals of a quadrilateral are the same length) holds for all squares and rectangles, so it does not give any particular insight into how to use Pythagorean Theorem to calculate the length of the diagonals.

Statement 2, however, is sufficient. In quadrilaterals, when the diagonals intersect at a 90-degree angle, the quadrilateral is a rhombus, square, or "kite." But since this shape is already known to have all 90-degree angles, it is already known to be a rectangle, so this fact tells you that the shape has to be a square, which allows you to calculate each side as 16, and use the principle of isosceles right triangles to calculate the diagonals at 16√2.

Answer: B.

achenguelly · Answer

Hello Bunuel,

How do you deduce that each side equal to 8? If we have a square and a perimeter of 64 that means 4*a=64 which gives 16.

Thank you

Regards

Bunuel · Answer

You are right. Veritas Prep solution has a typo. Edited. Thank you for noticing.

Chakolate · Answer

Statement 1 makes the quadrilateral a square or a rectangle, insufficient.

Statement 2 makes the quadrilateral a square or a rhombus, sufficient.

Answer B.

bumpbot · Answer

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If quadrilateral ABCD, pictured above, has a perimeter of 64, what is

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GMAT Data Sufficiency (DS) Questions

If quadrilateral ABCD, pictured above, has a perimeter of 64, what is

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