Question

If XYZ,XY=8cm,YZ=10cm xz=6cm if XYZ PQR and PQ=4cm then find the length of remaining sides of PQR​

Answer 1

Answer:

QR=(5cm),PR=(3cm)

(PQ)=½(XY):PQ=½×8=4cm

similarly,QR=½YZ:QR=½×10=5cm

PR=½XZ:PR=½×6=3cm

Answer 2

Given: In ΔXYZ, XY = 8 cm, YZ = 10 cm, XZ = 6 cm, ΔXYZ ~ ΔPQR and PQ = 4 cm.

To find: The length of remaining sides of PQR​.

Solution:

The symbol ' ~ ' means that the triangles XYZ and PQR are similar. When two triangles are said to be similar, their corresponding sides are in proportion and their corresponding angles are the same. In simple words, they differ only in size, not in shape. Hence, the corresponding sides can be written as follows.

$\frac{XY}{PQ} = \frac{YZ}{QR} = \frac{XZ}{PR}$

$\frac{8 cm}{4 cm} = \frac{10 cm}{QR} = \frac{6 cm}{PR}$

When rearranged, the value of QR  and PR is calculated as,

$QR = \frac{4 * 10}{8}$

      $= 5 cm$

$PR = \frac{6 * 4}{8}$

      $= 3 cm$

Therefore, the length of remaining sides of PQR​ is 5 cm and 3 cm.

Although part of your question is missing, you might be referring to this full question:  

In ΔXYZ, XY = 8 cm, YZ = 10 cm, XZ = 6 cm. If ΔXYZ ~ ΔPQR and PQ = 4 cm, then find the length of remaining sides of ΔPQR​.