Question

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

Answer 1

$\begin{array}{cc}\left(1\right)\Delta PQR\sim \Delta PST& \\ \angle RPQ=\angle TPS& \left\{common\right\}\\ \frac{PR}{PT}=\frac{PQ}{PS}& \left\{\frac{6}{3}=\frac{8}{4}\to \left(i\right)\left(Given\right)\right\}\end{array}$

So, By SAS similarity creterio.

$\Delta PQR\sim \Delta PST$ Proved.

$\begin{array}{cc}\left(2\right)\frac{QR}{ST}=2& \left\{From\left(i\right)ByC.P.S.T\right\}\\ \frac{5.8}{ST}=2& \\ \frac{5.8}{2}=ST& \\ 2.9=ST& \end{array}$