Question

In the figure, xy/qr and px/xq= py/yr=1/2, finf xy:qr

Answer 1

when the xy / qr = PX/Xq= py/yr= 1/2,
then 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

Now,  In ΔPQR and ΔAXY

∠P = ∠P         ( common )

∠PXY = ∠PQR   ( Corresponding angles are equal )

∠PYX = ∠PRQ    ( Corresponding angles are equal )

⇒ ΔPQR is similar to ΔAXY by AAA 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