A flower garden is to be laid out in the shape of a triangle. You are applying for a spring and summer job as gardener for this future garden. The owner is giving you a test to decide if you should have the job, which will include laying out the garden itself. Here is what you are being told about this triangle. It will have an obtuse angle. The three sides of the triangle will be whole numbers (measured in yards). The two shortest sides will be 3 and 4 yards respectively.
How long will the longest side be?
Solution
The longest side of the triangle must be longer than 4 (which we are told is one of the short sides) and less than 7 (the sum of the short sides has to be longer than the longest side). Between 4 and 7 are just two whole numbers: 5 and 6. The answer can't be 5 because then the triangle would be a right triangle (and have no obtuse angle). So the answer, by the process of elimination, is 6.
Now, assuming you get the job, how would you actually lay out that triangle on the ground?