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ABCD is a rectangle

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ABCD is a rectangle [#permalink] New post   13 Aug 2022, 09:10
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Attachment:
GRE area rectengle.jpg
GRE area rectengle.jpg [ 17.68 KiB | Viewed 2249 times ]


ABCD is a rectangle

Quantity A
Quantity B
Area of triangle AED
Area of triangle ABE + area of triangle ECD


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

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C
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B
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Re: ABCD is a rectangle [#permalink] New post   21 Aug 2022, 01:31
1
The rectangle ABCD can be divided into 3 triangles : ABE , AED and ECD.

From the diagram we can see that area of AED = area of ( ABE + ECD).

Hence, the answer is C.
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Re: ABCD is a rectangle [#permalink] New post   21 Aug 2022, 06:07
How was that helpful?????
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Re: ABCD is a rectangle [#permalink] New post   21 Aug 2022, 06:42
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helesashams wrote:
How was that helpful?????


All the angles labeled are 90°

The two small portions must be in sum equal to the big one triangle

C is the answer
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Re: ABCD is a rectangle [#permalink] New post   21 Aug 2022, 06:56
3
Carcass wrote:
Attachment:
GRE area rectengle.jpg


ABCD is a rectangle

Quantity A
Quantity B
Area of triangle AED
Area of triangle ABE + area of triangle ECD


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


First recognize that AB is the height of the rectangle ABCD AND AB is the height of triangle AED.

So the area of rectangle ABCD = (AD x AB)
And the area of triangle AED = (1/2)(AD x AB)
In other words, the area of triangle AED is HALF the area of rectangle ABCD
This means the area taken up by triangles ABE and ECD must take up the other HALF of the area of rectangle ABCD.
This means the two quantities are equal.

Answer: C
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Re: ABCD is a rectangle [#permalink]
21 Aug 2022, 06:56
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