On a segment CD with a length of 40 cm, points P and Q were marked so that CP = 28 cm

On a segment CD with a length of 40 cm, points P and Q were marked so that CP = 28 cm, QD = 26 cm. What is the length of the segment PQ?

Given:
CD – segment;
CD = 40 cm;
PM P and Q ∈ CD;
CP = 28 cm;
QD = 26cm;
PQ =?
Solution:
Points P and Q divide segment CD into three segments: CP, PQ and QD.
Because CP + QD ˃ CD, so point P is closer to point C, and point Q is closer to point D. Then we compose the following equalities:
CQ + PQ + DP = CD;
CQ + PQ = CP hence CQ = CP – PQ;
DP + PQ = QD hence DP = QD – PQ;
CP – PQ + PQ + QD – PQ = CD;
CP + QD – PQ = CD;
CP + QD – CD = PQ;
PQ = CP + QD – CD;
PQ = 28 + 26 – 40 = 14 (cm);
Answer: PQ = 14 cm.



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