Interview Question: No, Not the Bermuda Kind

Sample Question #199 (mathematics – geometry)

[For some reason, triangle questions are popular at quant interviews, especially at hedge funds]

Can you prove the following facts about a triangle?

  1. The total length of any two sides of a triangle is larger than the third side
  2. The difference in length between any two sides is smaller than the third side
  3. The three angles must add up to 180 degrees
  4. In a right triangle, a2+b2=c2, where a and b are the two right sides.

(Comment: I believe the purpose of questions like this is to see if you can think, and recall stuff you learned a long, long time ago, on your foot)

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2 Responses to Interview Question: No, Not the Bermuda Kind

  1. Brett says:

    ANSWER
     
    1. It’s probably sufficient to provide a visual proof.
    2. Follows immediately from #1.
    3. Many ways; one way is to say a triangle is half of a parallelogram.
    4. This one is hard…
     

  2. Unknown says:

    4. You can prove this one with a visual.
     Draw a square and pick a point at the same spot on each line. Call the smaller section a and call the larger section b. Now, if you were to connect the dots, you would be left with 5 shapes inside of the square. 4 trianges with sides a and b and a square in the middle. We will label each side of the square, c. Now, let see what we have. The area of the total square is a^2 + 2ab + b^2, because it’s simply (a + b)^2. The inside is 4 * (.5ab) = 2ab, from the four triangles, and c^2 from the square. Let’s set up our equation: a^2 + 2ab + b^2 = 2ab + c^2. The proof follows.

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