Points A and B are the midpoints of the sides PQ and QR of the PQR triangle.

| July 4, 2021 | education

Points A and B are the midpoints of the sides PQ and QR of the PQR triangle. Find the perimeter of triangle PQR if the perimeter of triangle AQB is 38 cm.

Given: a triangle, where AP = AQ, BR = BQ and AB + AQ + BQ = 38 cm. It is necessary to determine the perimeter of the triangle PQR, that is, PR + PQ + RQ.
We have PQ = AP + AQ = AQ + AQ = 2 * AQ, similarly, RQ = BR + BQ = BQ + AQ = 2 * BQ.
Since points A and B are the midpoints of the sides PQ and QR (respectively) of the triangle PQR, then according to the definition of the midline of the triangle, the segment AB is the midline of the triangle PQR.
Using the properties of the middle line of the triangle, we can assert that AB = PR / 2 or PR = 2 * AB.
We have PR + PQ + RQ = 2 * AB + 2 * AQ + 2 * BQ = 2 * (AB + AQ + BQ) = 2 * 38 cm = 76 cm.
Answer: 76 cm.



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