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IGCH in terms of x

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IGCH in terms of x

by sanju09 » Wed Sep 15, 2010 8:27 pm
If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x?
(A) 4 x + 12
(B) 7 x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

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by niksworth » Thu Sep 16, 2010 6:35 am
This question requires an assumption that EG || AB and FH || AD, which is not stated explicitly in the question.

Now,
Area of ABCD = x^2 = x*x
Since ABCD is a square, side of the square has to be x.

AE = 4 => ED = x-4
AF = 3 => FB = x-3

Using parallelism,
IH = x-4
IG = x-3

Therefore,
Area of IGCH = (x-4)(x-3) = x^2 - 7x + 12.

Thus, E.
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by sanju09 » Thu Sep 16, 2010 8:07 pm
niksworth wrote:This question requires an assumption that EG || AB and FH || AD, which is not stated explicitly in the question.

Now,
Area of ABCD = x^2 = x*x
Since ABCD is a square, side of the square has to be x.

AE = 4 => ED = x-4
AF = 3 => FB = x-3

Using parallelism,
IH = x-4
IG = x-3

Therefore,
Area of IGCH = (x-4)(x-3) = x^2 - 7x + 12.

Thus, E.
You are utterly correct, with nothing edifying given in the attachment, the stem must read like following

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x? (All corners are at right angle in the attached figure below)
(A) 4 x + 12
(B) 7 x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12
The mind is everything. What you think you become. -Lord Buddha



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Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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by goyalsau » Fri Sep 17, 2010 12:10 am
One more E.
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by brijesh » Sun Sep 19, 2010 7:51 am
sanju09 wrote:If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x?
(A) 4 x + 12
(B) 7 x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

[spoiler]Source: https://readyforgmat.com[/spoiler]
Its E
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