A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ=12.5 cm,PA=5 cm,BR=6 cm and PB=4 cm. Is AB∥QR? Give reasons for your answer.

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Rajan@2021Guru

Asked: March 26, 20212021-03-26T11:25:03+05:30 2021-03-26T11:25:03+05:30In: ICSE

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MathsMentor · Answer 1 · 2021-03-27T19:35:07+05:30

MathsMentor Guru

PQ = 12.5 cm PA = 5 cm BR = 6 cm PB = 4 cm

Then, QA = QP – PA = 12.5 – 5 = 7.5 cm

So, PA/AQ = 5/7.5 = 50/75 = 2/3 … (i) PB/BR = 4/6 = 2/3 … (ii)

Form Equations (i) and (ii).

PA/AQ = PB/BR

We know that, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Therefore, AB || QR.