Hi,
Already this question has been clearly explained above.
Just adding only one point, instead of “x” as the area of triangle, we can use some values for faster calculation (only for those who are very comfortable with numbers than variables).
BC = AD = 5(Given)
Area of rectangle = length * breadth = 5 * AB = 5 * AB
We need to find the value of AB.
Triangles EGF and ADF are similar triangles (EF and AB are parallel to each other).
In similar triangles, angles are equal and sides are proportional.
EG / AD = 2/5
So, height of these two triangles are also similar,
So, if we consider, height of the triangle EGF as 4,
Then given of the triangle EGF = x = ½ * 2 * 4 = 4
So, x = 4
According to the similar triangle rule,
Heights should also be in the ratio of 2/5 = 4/ 10
Breadth of the rectangle ABCD = Height of the triangle ADF – Height of the triangle EGF = 10 – 4 = 6
So the area of rectangle = 5 * 6 = 30.
Just substitute x = 4 in the answer choices, and check where the answer is 30.
A. 5x - 20
B. 5x/2 - 10
C. 15x - 60
D. 15x/2 - 30
E. 25x/2 – 25
So answer is D.
Hope this helps.
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GMAT Mentors