For this week’s brain twister, we have a multiple-answer question. As the directions state, you need to choose every answer choice that applies to the question. For a truly twisted experience, see if you can do this question without a calculator.

Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

Indicate all such values

(A) 119/359

(B) 359/119

(C) π

(D) 16

Be sure to check the GRE Blog on Thursday for the explanation!

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we can find lowest area which will be formed by a triangle whose side will be 2,8,8 .Area of this triangle will be 7.9 sqr. to find maximum area we we have to form a right angled triangle which is not possible in this case (perimeter 18) . so we can assume maximum area will be of equilateral triangle. which will be 15.598 . and non of the above answer comes in the range of 7.9 to 15.598

Option looks like pie (3.14), in which case, my answer would be option D only.

Area of a triangle is maximum when it is equilateral. Therefore, for an equilateral triangle with perimeter 18, side = 6, and hence, area= (root(3)/4) * (6*6) = 15.something..

Hence, the area of the triangle could be anything from zero up to 15.something.

Thus, the area cannot be 16.

My GRE is on 21 Aug..These problems and the others on this website really keep me going! Thanks a lot! 🙂

Ans : D

Reason : Given the perimeter, the equilateral triangle will have the maximum area. The maximum possible area(each side 6) is 9*(root of 3) which is 15.888.Hence D cannot be the area.

For a given perimeter, an equilateral triangle can have the maximum area. Option D violates this.

The answer is D

The simple logic is that , for a specific perimeter of a triangle , the equilateral triangle has the greatest area.

Therefore , the maximum area would be 9root3 or 15.58.

Any area less than this and greater than 0 is acceptable .

So the only option which goes beyond the maximum area is option D (16) , so is the answer.