The triangle above has side DC of the square as its base. What is the

Question

https://gmatclub.com/forum/download/file.php?id=35200 The triangle above has side DC of the square as its base. What is the area of the shaded region? (1) DM = 5 (2) M is the midpoint of side AB 2017-05-14_2254.png

Kurtosis · Answer

St1: DM = 5 --> Clearly insufficient as we do not know any other information about the triangle.

St2: M is the midpoint --> Drop a perpendicular from M to DC. We can get to know that the 4 resulting triangles are congruent.
Area of shaded region = Area of MCD
We do not have any data on the sides of the square or triangle.
Not Sufficient.

Combing St1 and St2; MD^2 = a^2 + a^2/4
25 = 5a^2/4 --> a^2 = 20
Area of shaded region = a^2/2 = 10

Answer: C

GMATinsight · Answer

The shaded region = Area of square - Area of Triangle CDM = ?

Statement 1  : DM = 5

This statement doesn't help us find the area of triangle or area of the square hence
NOT SUFFICIENT

Statement 2  : M is the midpoint of side AB

This statement doesn't help us find the area of triangle or area of the square hence
NOT SUFFICIENT

Combining the two statements  
Since M is the midpoint so triangle DMC becomes an isosceles triangle with height equal to the base 
Now using pythagorus theorem both base and height which inturn are equal to the side of the square can be calculated leading to area of both square and triangle hence
SUFFICIENT

Answer: option C

vijaisingh2001 · Answer

area of a triangle is base * height/2

since M is on the other side of the square ( doesn't matter whether M is the midpoint or somewhere on the edge of the square. the height of the triangle will be the same since it is a square so the height of the triangle is same as the one side of the square

so answer should be A rather than C

ashygoyal · Answer

But with statement 1, can you get a numeric answer for the area? No.

Therefore, you have to use both statements, to get a numerical answer to the question. Hence C suffices.

Thanks and Regards, 
ashygoyal

bumpbot · Answer

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The triangle above has side DC of the square as its base. What is the

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