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Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Rectangles ABCD and EFGH have equal areas. What is the length of side  [#permalink]

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Difficulty:   5% (low)

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

HideShow timer Statistics 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 [ 22.88 KiB | Viewed 631 times ]

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

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Bunuel wrote: 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.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4001
Re: Rectangles ABCD and EFGH have equal areas. What is the length of side  [#permalink]

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Top Contributor
Bunuel wrote: 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. 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

Cheers,
Brent
_________________ 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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