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What is the area of the rectangle ABCD? (1) BD = 5 (2) AC = 5/3*BC

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What is the area of the rectangle ABCD? (1) BD = 5 (2) AC = 5/3*BC  [#permalink]

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New post 06 Sep 2018, 23:47
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

82% (02:10) correct 18% (01:19) wrong based on 37 sessions

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Re: What is the area of the rectangle ABCD? (1) BD = 5 (2) AC = 5/3*BC  [#permalink]

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New post 07 Sep 2018, 00:58
Bunuel wrote:
Image
What is the area of the rectangle ABCD?


(1) BD = 5

(2) AC = 5/3*BC


Attachment:
image016.jpg


QUESTION: What is the area of the rectangle ABCD?

Statement 1: BD = 5

Wit the help of diagonals, we can't calculate the area of the rectangle because the angle between the diagonals is unknown hence

NOT SUFFICIENT

Statement 2: AC = 5/3*BC

This statement gives us the ratio of the lengths of sides of rectangle no exact dimension hence

NOT SUFFICIENT

Combining the two statements
Let, BC = x
AC = (5/3)x
i.e. \(AB = √{(25x^2/9)-(x^2)]\)

Also, AC = BD = (5/3)x = 5

i.e. x is unknown which can get us the exacl length and width as well hence we can calculate the area of the rectangle hence

SUFFICIENT

Answer: Option C
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Re: What is the area of the rectangle ABCD? (1) BD = 5 (2) AC = 5/3*BC  [#permalink]

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New post 08 Sep 2018, 10:41
Bunuel wrote:
Image
What is the area of the rectangle ABCD?


(1) BD = 5

(2) AC = 5/3*BC


Attachment:
image016.jpg


S1 - BD=5
Insufficient.

S2 - AC = 5/3*BC.
We don't have any values. Insufficient.

Combining,
AC=BD ; \(AB^2+BC^2=AC^2 = BD^2 = 25\)
BC = 3/5 AC.
We can find AB and hence the area.
Answer C.
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Re: What is the area of the rectangle ABCD? (1) BD = 5 (2) AC = 5/3*BC   [#permalink] 08 Sep 2018, 10:41
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