Problem Solving

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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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.

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

One more E.

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