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Rectangles ABCD and EFGH have equal areas. What is the length of side

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Rectangles ABCD and EFGH have equal areas. What is the length of side  [#permalink]

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New post 19 Dec 2018, 00:33
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (00:52) correct 10% (00:34) wrong based on 41 sessions

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D
Joined: 31 Oct 2013
Posts: 1471
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
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Re: Rectangles ABCD and EFGH have equal areas. What is the length of side  [#permalink]

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New post 19 Dec 2018, 00:44
Bunuel wrote:
Image
Rectangles ABCD and EFGH have equal areas. What is the length of side FG?


A. 1
B. 2
C. 3
D. 4
E. 6

Attachment:
Capture (2).JPG



Area of ABCD:

\(a^2 + b^2 =c^2\)

\(8^2 + b^2 = 10^2\)

\(b^2 = 36\)

b =6.

Area = 6*8 =48.

Now we can find out the area of EFGH.

12*x = 48

x =4.

D is our answer.
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Re: Rectangles ABCD and EFGH have equal areas. What is the length of side  [#permalink]

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New post 06 Jul 2019, 08:29
Top Contributor
Bunuel wrote:
Image
Rectangles ABCD and EFGH have equal areas. What is the length of side FG?


A. 1
B. 2
C. 3
D. 4
E. 6

Attachment:
Capture (2).JPG


Since ABCD is a rectangle, we can see we have a right triangle hiding in the diagram.
Image
So, we can use the Pythagorean Theorem (or Pythagorean triplets) to find the length of CD
Once we know that CD = 6, we can find the area of ABCD

Area of rectangle ABCD = (base)(height) = (8)(6) = 48

This means the area of rectangle EFGH = 48
Since rectangle EFGH has a height of 12, we know that its base must have length 4 (since 12 x 4 = 48)

In other words, side FG must have length 4

Answer: D

Cheers,
Brent
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Re: Rectangles ABCD and EFGH have equal areas. What is the length of side   [#permalink] 06 Jul 2019, 08:29
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Rectangles ABCD and EFGH have equal areas. What is the length of side

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