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# ABCD is a quadrilateral. Find the area-Geometry-DS

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24 Aug 2018, 20:42
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Difficulty:

45% (medium)

Question Stats:

49% (00:52) correct 51% (00:37) wrong based on 41 sessions

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(1) The diagonals are perpendicular bisectors of each other.

(2) The length of each side is 10 cm.

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24 Aug 2018, 23:29
Harshgmat wrote:

(1) The diagonals are perpendicular bisectors of each other.

(2) The length of each side is 10 cm.

S1 - The diagonals are perpendicular bisectors of each other. - Can be a square or rhombus.
Cannot find the area. Insufficient.

S2 - The length of each side is 10 cm. Cannot find the area. Insufficient.
Combining S1 and S2 - Can be a square or rhombus.
Cannot find the area. Insufficient.

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25 Aug 2018, 00:08
Harshgmat wrote:

(1) The diagonals are perpendicular bisectors of each other.

(2) The length of each side is 10 cm.
St1: perpendicular bisector means diagonals intersect at 90 degrees and the point where they intersect is mid point of the diagonal.

Possible figures : Rhombus or square

St2: each side is equal - - - > possible figure is rhombus or square.

Combined -
Can be square or rhombus

E
____________

On a side note : if it was mentioned diagonals intersect each other at 90---possible figures were kite, rhombus, square,

Diagonals are equal in length - - - possible figures were square, rectangle, and isosceles trapenzium.

Consider kudos if that helped

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25 Aug 2018, 02:05
Harshgmat wrote:

(1) The diagonals are perpendicular bisectors of each other.

(2) The length of each side is 10 cm.

St1:- The diagonals are perpendicular bisectors of each other.
I would discard this statement immediately without thinking about geometric properties. Area is a numerical value, there must be a numerical value in the statements(This is a minimum requirement).
Insufficient.

St2:- The length of each side is 10 cm.
Area is Y1,Y2,Y3 etc, when the quad is a rhombus, where $$0<Area(Y)\leq{10^2}$$
(This range of areas is due to the flexibility of a rhombus that fits it at different angles. Max area=$$10^2$$ when the angles of the rhombus are at 90 degree ).
No unique value of area.
Insufficient.

Combining, no new information as diagonals of both rhombus and square are perpendicular bisector of each other.
Same scenario as we have cited in st2.
No unique value of area, insufficient.

Ans. (E)
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ABCD is a quadrilateral. Find the area-Geometry-DS   [#permalink] 25 Aug 2018, 02:05
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