Question

On triangle PQR X and Y are two points on PQ and PR if XY// QR and PX/XQ=PY/YR=1/2,then find XY:QR

Answer 1

Since the XY||QR
angle X = angle Y
and
PX/XQ=PY/YR
trianglePQR is similar to trianglePXY
Hence we know that
PX/XQ=PY/YR=XY/QR=1/2
So,
XY/QR=1/2

Answer 2

Answer:

XY : QR = 1 : 3

Step-by-step explanation:

Given: Δ PQR     , Point X and Y are on sides PQ and PR,

          XY || QR

To find: XY : QR

In Δ PQR

∠PXY = ∠PQR   ( Corresponding angles are equal )

∠PYX = ∠PRQ    ( Corresponding angles are equal )

Now,  In ΔPQR and ΔAXY

∠P = ∠P  ( common )

∠PXY = ∠PQR   ( from above )

∠PYX = ∠PRQ    ( from above )

⇒ ΔPQR ~ ΔAXY by AAA similarity Criteria.

We get,

$\frac{PX}{PQ}=\frac{PY}{PR}=\frac{XY}{QR}$

Given,

$\frac{PX}{XQ}=\frac{PY}{YR}=\frac{1}{2}$

⇒ PQ = 1 + 2 = 3

So, $\frac{PX}{PQ}=\frac{1}{3}=\frac{PY}{PR}=\frac{XY}{QR}$

Therefore, XY : QR = 1 : 3