In the adjoining figure (not drawn to scale),
$P S = 4 c m, S R = 2 c m, P T = 3 c m$ and $Q T = 5 c m$ ,
(i) Show that $△ P Q R \sim △ P S T$ .
(ii) Calculate $S T$ , if $Q R = 5 \cdot 8 c m$

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Solution

$\begin{matrix} (1) Δ P Q R \sim Δ P S T ∠ R P Q = ∠ T P S & {c o m m o n} \frac{P R}{P T} = \frac{P Q}{P S} & {\frac{6}{3} = \frac{8}{4} \to (i) (G i v e n)} \end{matrix}$
So, By SAS similarity creterio.
$Δ P Q R \sim Δ P S T$ Proved.
$\begin{matrix} (2) \frac{Q R}{S T} = 2 & {F r o m (i) B y C . P . S . T} \frac{5.8}{S T} = 2 \frac{5.8}{2} = S T 2.9 = S T \end{matrix}$

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In the adjoining figure (not drawn to scale), PS=4 cm,SR=2 cm,PT=3 cm and QT=5 cm,(i) Show that △PQR∼△PST.(ii) Calculate ST, if QR=5⋅8 cm

(1)ΔPQR∼ΔPST∠RPQ=∠TPS{common}PRPT=PQPS{63=84→(i)(Given)}So, By SAS similarity creterio.ΔPQR∼ΔPST Proved.(2)QRST=2{From(i)ByC.P.S.T}5.8ST=25.82=ST2.9=ST

In the adjoining figure (not drawn to scale),
$P S = 4 c m, S R = 2 c m, P T = 3 c m$ and $Q T = 5 c m$ ,
(i) Show that $△ P Q R \sim △ P S T$ .
(ii) Calculate $S T$ , if $Q R = 5 \cdot 8 c m$