According to Prashant Bagdia, a computer science student at the National Institute of Technology in Warangal, India, his friend was asked the following question during a campus placement interview with Microsoft. For those of you who don’t know basic geometry, good luck getting the question right – and for those of you who do, well…good luck anyway. You probably won’t get it right either:
Interviewer: Ok, so one last question. A right triangle has a hypotenuse equal to 10 and an altitude to the hypotenuse equal to 6. Find the area of the triangle
My friend started thinking ‘Why would a software company ask a geometry question and that too such a trivial one! Maybe it is a trick question!? Maybe it isn’t a trick question and he just wants me to think otherwise so that I would screw up even this paltry question!?’
He contemplated for a while and answered:
Friend: Sir, as area of any triangle is 0.5*base*height, the answer to this question would be 0.5 *10*6 which evaluates to 30!
Interviewer: Are you sure? Think about it again!
*My friend thought for a while and replied with full confidence*
Friend: Yes sir, I am sure the area of triangle is 30. You are just messing up with my brain to make me think otherwise so that I would commit error even in this trivial question.
For those of you trying to picture it, this is what the triangle would look like:
Spoiler alert: the answer his friend gave is wrong. Can you figure out why?
According to Prashant, it’s because it’s impossible for that type of triangle to exist:
Here’s the solution: It turns out that the maximum length of the altitude to hypotenuse in the above triangle can only be 5 and not 6, so its maximal area would be 25.
The angle opposite the hypotenuse must be a right angle of 90 degrees. This means the two sides of the triangle must subtend a 180 degree angle in a circle. The hypotenuse must be the diameter of a circle, and the third point can be any point on the circle (except the endpoints of the hypotenuse).
The vertical distance from the third point to the hypotenuse is the altitude to the hypotenuse. This is largest when the third point is at the top or bottom of the circle, and the vertical distance is equal to the radius of the circle (half the length of the hypotenuse, which is the diameter of the circle).
Therefore, a right triangle with a hypotenuse of 10 can have an altitude on its hypotenuse of at most 5.
Suffice to say, Prashant’s friend did not get the job.
But did you fare any better? Let us know in the comments!