Question

in Δxyz , xy=8cm , yz = 10cm, xz = 6cm if δxyz ~ Δpqr and pq = 4 then find the lengths of remaining sides​

Answer 1

Step-by-step explanation:

Given:-

in Δxyz , xy=8cm , yz = 10cm, xz = 6cm

Δ xyz ~ Δpqr and pq = 4

To find:-

length of pr and qr

Solution:-.

According to Thales theorem

if

Δ xyz ~ Δpqr

then

${\boxed{{\frac{xy}{pq}}={\frac{yz}{qr}}={\frac{xz}{pr}}}}$

$\implies{{\frac{8}{4}}={\frac{10}{qr}}={\frac{6}{pr}}}$

$\implies{{\frac{8}{4}}={\frac{10}{qr}},\:{\frac{8}{4}}={\frac{6}{pr}}}$

$\implies{2={\frac{10}{qr}},\:{2={\frac{6}{pr}}}}$

$\implies{qr={\frac{10}{2}},\:{pr={\frac{6}{2}}}}$

$\implies{\underline{\boxed{\bf{{qr=5cm,pr=3cm}}}}}$

Answer 2

Step-by-step explanation:

Consider, Δ XYZ ~ Δ PQR

∴XYPQ=YZQR=XZPR

⇒48=6QR=5PR

⇒48=6QR and

48=5PR

⇒ QR = 12 cm and PR = 10 cm

Hence, the lengths of remaining sides of Δ PQR are 12 and 10 cm.