On the segment AM = 22 cm, we marked the point K, such that AK = 16 cm, and the point P

On the segment AM = 22 cm, we marked the point K, such that AK = 16 cm, and the point P, such that PM = 17 cm. Find the length of the segment KP.

This problem can be solved in two ways. Let’s consider each of them.

Method 1:
Since AM = 22 cm; AK = 16 cm; MP = 17 centimeters, then the RK will be located in the zone of both the segment AK and MP.
Therefore, if we subtract the sum AK + MP from the total length of the segment, we get the length of the segment KP:
PK = (AK + PM) – AM;
PK = (16 + 17) – 22;
PK = 33 – 22;
PK = 11 (centimeters).
Method 2:
We can find residual segments from large segments that are in the main segment. Namely:
AP = AM – MP;
AP = 22 – 17 = 5 (centimeters).
KM = AM – AK;
KM = 22 – 16 = 6 (centimeters).
Thus, if we add the segments KM and AP and subtract them from the main segment AM, then we get the segment KP:
KP = AM – (KM + AP);
KP = 22 – (6 + 5);
KP = 22 – 11;
KP = 11 (centimeters).
Answer: 11 centimeters.