Question

In the figure, given below, PQR is a right-angle triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.

Answer 1

Given that `(PX)/(XQ) = 1/2` and XY || QR

So, `(PX)/(XQ) = (PY)/(YR) = 1/2`

Since PY = 4 cm, YR = 8 cm.

Hence, PR = 12 cm

Since ΔPQR is a right-angled triangle

By Pythagoras theorem,

QR² = PR² – PQ²

`=>` QR² = 12² – 6²

`=>` QR² = 144 – 36

`=>` QR² = 108

`=>` QR = 10.39 cm