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ABCE is a square, and BCDE is a parallelogram.

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ABCE is a square, and BCDE is a parallelogram. [#permalink] New post 11 Dec 2017, 02:46
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ABCE is a square, and BCDE is a parallelogram.

Quantity A
Quantity B
The area of square ABCE
The area of parallelogram BCDE


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: ABCE is a square, and BCDE is a parallelogram. [#permalink] New post 14 Jan 2018, 02:32
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let us suppose a side of the square = s
then, the area of the square would be s^2
Diagonal BE of the square is the hypotenuse of the triangle BAC
Since the triangle is a 45-45-90 triangle the hypotenuse must measure s√2
For the parallelogram notice that the area of the parallelogram = area of triangle BCE and area of triangle CED
Side BE//CD and CE is the transversal so triangle BCE and triangle CED are similar
<BCE=<CED=90degree
<BEC=<ECD
Since the two triangle share the same side the triangles have equal length of sides. This follows
area of parallelogram = 2* area of triangle BCE
area of triangle BCE= 1/2*s*s=s^2/2
area of parallelogram = s^2/2*2= s^2
area of square = area of parallelogram
(c)
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Re: ABCE is a square, and BCDE is a parallelogram. [#permalink] New post 14 Jan 2018, 11:51
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Added the OA. It is C.

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Re: ABCE is a square, and BCDE is a parallelogram.   [#permalink] 14 Jan 2018, 11:51
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ABCE is a square, and BCDE is a parallelogram.

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