In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are

According to the information given in the question stem, EF is perpendicular to AB (EF || AD), and \(AE * GE = 2 * EF * EB\) ( the area of triangle AEG is half of the area of triangle FEB ). Now to further calculate the area of the rectangle ABCD, I would like to know the product of length and breadth of the rectangle. Let me assume, breadth CB = AD = x, and length AB = CD = y.

1) According to first statement, EB = EF = x = 5.
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * EG = 2 * 5^2\)
Since we do not know the measure of AE and EG, this information is insufficient.

2) According to second statement, EF = CB = x, but EG = \(1/2\).x
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * 1/2 * x = 2 * x * EB\)
Solving this, I get AE = 4 EB. Furthermore, y = AE + EB = 5 EB.
But we do not have the value of EB.
Thus, this information is also insufficient, since it only helps us getting values in ratios and variables.

Combining both information in 1 and 2, I can find the answer to the question. In (1) we got EB = x = 5, and in (2) we got y = 5 EB, so y = 25. Therefore, option C is the correct answer.