ABCD is a quadrilateral. A rhombus is a quadrilateral whose sides are

Question

ABCD is a quadrilateral. A rhombus is a quadrilateral whose sides are all congruent. BCEF is a rhombus and shares a common side with the quadrilateral ABCD. The area of which one is greater: ABCD or BCEF ?

(1) ABCD is a square.
(2) BCEF is not a square.

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p05eid0n · Answer

Given
ABCD is a quadrilateral. 
BCEF is a rhombus.

Statement 1 - ABCD is a square.
Since ABCD and BCEF share a side BC, we can conclude that the lengths of sides are the same.
But we cannot conclude that BCEF is truly only a rhombus because every square is also a rhombus.

so, BCEF can be a square or a rhombus. So statement 1 is insufficient.

Statement 2 - BCEF is not a square.
This gives us a on clarity on BCEF but doesn't mention anything about ABCD
So statement 2 is insufficient.

Combining 1 and 2
we now know that ABCD is a square and BCEF is only a rhombus.
for a square and rhombus with equal sides, square will have max area.

IMO C

yashikaaggarwal · Answer

Both ABCD and BCEF share 1 side 
1) ABCD is a square
Case 1: BCEF is a square
Both ABCD and BCEF have same area.

Case 2: BCEF is a rectangle
ABCD have bigger area.(Since square have the greatest area among all quadrilaterals)
(Insufficient)

2) BCEF is not a square.
Case 1: ABCD is a square
ABCD have bigger area

Case 2: ABCD is also not a square, there are many possible figure of ABCD and BCEF, I.e. Rectangle, Trapezoid, Trapezium, Rhombus. Varying the area among each other.
(Insufficient)

Combining both.
ABCD is a square and BCEF is a non square.
Therefore area of ABCD is bigger.
(Sufficient)

Answer is C

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AjitJangale · Answer

Important Property = For a given perimeter square have always largest area.

We need to identify ABCD and BCEF are exactly square or rhombus or any other quadrilateral.

Statement 1) ABCD is a square.

Not given about exactly about BCEF.

Insufficient

(2) BCEF is not a square.

This does not give that BCEF and ABCD are which type quadrilateral.

Insufficient.

Combining Together we know that ABCD is square and BCEF is not square. So we can conclude that ABCD have greater area than BCEF as mentioned in above property.

IMO Answer is C,

sambitspm · Answer

Kindly see the attachment.

Area of Rhombus is x^2*sin⨁

bumpbot · Answer

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ABCD is a quadrilateral. A rhombus is a quadrilateral whose sides are

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