Given a triangle KMN, a straight line is drawn through point O on the side KN and point P on the side KM

univerkov | March 15, 2021 | education

Given a triangle KMN, a straight line is drawn through point O on the side KN and point P on the side KM, and Op is parallel to MN. Find the length of the segment OP if you know that: MN = 20 PK = 12 KM = 16.

1. Line OP intersects two sides of the triangle (KM and KN) and is parallel to the third (MN) according to the problem statement. Therefore, the KRO triangle is similar to the KMN triangle.

2. Based on this, we make up the proportion (the ratio of similar sides):

KR / KM = PO / MN.

12/16 = RO / 20.

PO = 12 x 20/16.

РO = 15 units of measurement.

Answer: the length of the РO segment is 15 units.

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