Question

In the given figure ST ║ QR, PS = 2.4 cm, PT = 3.2 cm, TR = 4.8 cm, then find PQ.

Answer 1

Answer:

ST||QR

PS/SQ=PT/TR

2.4/SQ=3.2/4.8

sq=2.4×4.8/3.2=3.6cm

pq=PS+sq=2.4+3.6

pq=6cm

Answer 2

The value of $PQ$ is $6\ cm$

Step-by-step explanation:

Given,

In figure,

$ST\parallel QR,PS=2.4\ cm,PT=3.2\ cm\ and\ TR=4.8\ cm$

In $\triangle PST$ and $\triangle PQR$,

• $\angle PST=\angle PQR$ (∵ $ST\parallel QR$)

• $\angle PTS=\angle PRQ$ (∵ $ST\parallel QR$)

• $\angle P$ common.

∴ $\triangle PST$≅$\triangle PQR$

So,

$\frac{PS}{SQ}=\frac{PT}{TR}$

⇒$\frac{2.4}{SQ}=\frac{3.2}{4.8}$

⇒$SQ=\frac{2.4\times 4.8}{3.2}$

⇒$SQ=3.6\ cm$

∴ $PQ=PS+SQ=2.4+3.6=6\ cm$

So, The value of $PQ$ is $6\ cm$