Question

In the given figure, XY || QR, `(PQ)/(XQ) = 7/3` and PR = 6.3 cm. Find the length of YR.

Answer 1

Given:

In ΔPQR, XY || QR

`(PQ)/(XQ) = 7/3`

PR = 6.3 cm

To find: Length of YR

Since XY || QR, by Basic Proportionality Theorem (Thales Theorem):

`(PX)/(XQ) = (PY)/(YR)`

We are given `(PQ)/(XQ) = 7/3`.

We can write PQ as PX + XQ:

`(PX + XQ)/(XQ) = 7/3`

`(PX)/(XQ) + 1 = 7/3`

`(PX)/(XQ) = 7/3 - 1`

`(PX)/(XQ) = 4/3`

From BPT, we know:

`(PY)/(YR) = (PX)/(XQ) = 4/3`

Let PY = 4k and YR = 3k.

Given PR = 6.3 cm

PY + YR = 6.3

4k + 3k = 6.3

7k = 6.3

k = 0.9

Calculating YR:

YR = 3k

YR = 3 × 0.9

YR = 2.7 cm