Question

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.

Answer 1

Given,

PQ = 12.5 cm,

PA = 5 cm,

BR = 6 cm

And PB = 4 cm

Then, QA = QP – PA

= 12.5 – 5

= 7.5 cm

Now, `("PA")/("AQ")`

= `5/7.5`

= `50/75`

= `2/3`  ...(i)

And `("PB")/("BR")`

= `4/6`

= `2/3`  ...(ii)

From equations (i) and (ii),

`("PA")/("AQ") = ("PB")/("BR")`

By converse of basic proportionally theorem,

AB || QR