Question

in a triangle PQR xy is parallel to qr.if px:xq=1:3 and qr=9cm,find the length of xy

Answer 1

PX/QX=1/3
on reversing ,
QX/PX+1=3+1
PQ/PX=4
PQ/PX=QR/XY
QR/XY=4
9=4XY
XY=9/4

Answer 2

Answer:

Length of XY is 9/4 cm.

Step-by-step explanation:

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

          XY || QR and QR = 9 cm

To find: length of XY

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,

$\frac{PX}{XQ}=\frac{PY}{YR}=\frac{1}{3}$

⇒ PQ = 1 + 3 = 4

So, $\frac{PX}{PQ}=\frac{1}{4}=\frac{PY}{PR}=\frac{XY}{QR}$

$\frac{XY}{QR}=\frac{1}{4}$

$\frac{XY}{9}=\frac{1}{4}$

$XY=\frac{9}{4}$

Therefore, Length of XY is 9/4 cm.