A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?

 No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: