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

September 28, 2021 | education

| **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.